*Article* **Mechanical and Impact Properties of Engineered Cementitious Composites Reinforced with PP Fibers at Elevated Temperatures**

**Raad A. Al-Ameri 1 , Sallal Rashid Abid 2, \* and Mustafa Özakça 1**


**Abstract:** The repeated impact performance of engineered cementitious composites (ECCs) is not well explored yet, especially after exposure to severe conditions, such as accidental fires. An experimental study was conducted to evaluate the degradation of strength and repeated impact capacity of ECCs reinforced with Polypropylene fibers after high temperature exposure. Compressive strength and flexural strength were tested using cube and beam specimens, while disk specimens were used to conduct repeated impact tests according to the ACI 544-2R procedure. Reference specimens were tested at room temperature, while three other groups were tested after heating to 200 ◦C, 400 ◦C and 600 ◦C and naturally cooled to room temperature. The test results indicated that the reference ECC specimens exhibited a much higher failure impact resistance compared to normal concrete specimens, which was associated with a ductile failure showing a central surface fracture zone and fine surface multi-cracking under repeated impacts. This behavior was also recorded for specimens subjected to 200 ◦C, while the exposure to 400 ◦C and 600 ◦C significantly deteriorated the impact resistance and ductility of ECCs. The recorded failure impact numbers decreased from 259 before heating to 257, 24 and 10 after exposure to 200 ◦C, 400 ◦C and 600 ◦C, respectively. However, after exposure to all temperature levels, the failure impact records of ECCs kept at least four times higher than their corresponding normal concrete ones.

**Keywords:** repeated impact; ACI 544-2R; high temperatures; fire; ECC; impact ductility

#### **1. Introduction**

Regardless of the function and type of occupation of any structural facility, it is still probable to be subjected to unfavorable extreme or accidental loads. Most of the modern reinforced concrete structures are designed to withstand the usual design gravity loads in addition to lateral loads, such as wind and seismic loads. However, considering the accidental loading cases in design is not a typical procedure required by building design codes because this action would distend the construction cost. Among the most probable types of accidental loads are fires and impact loads. The rapid increase of temperature due to the combustion of furniture, nonstructural materials and electrical wiring can noticeably degrade the structural capacity of slabs, beams and columns. On the other hand, sudden impact loads can cause serious concentrated damage that may affect the integrity of the structure.

Although there are great advantages in fire resisting systems and materials in the construction industry, fires keep occurring every day. Large numbers of fire accidents are reported every year [1], where approximately half a million accidental fires were reported between 2013 and 2014 in the USA, while more than 150,000 fire accidents were reported in the UK during the same period. From these fires, 40% were recognized as structural fires [1,2]. Between 1993 and 2016, approximately 90 million fire accidents were recorded

**Citation:** Al-Ameri, R.A.; Abid, S.R.; Özakça, M. Mechanical and Impact Properties of Engineered Cementitious Composites Reinforced with PP Fibers at Elevated Temperatures. *Fire* **2022**, *5*, 3. https://doi.org/10.3390/fire5010003

Academic Editor: Maged A. Youssef

Received: 28 November 2021 Accepted: 26 December 2021 Published: 30 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

in 39 countries with more than a million death incidences [2]. The crucial question after each structural fire is whether the concrete structure can continue to be occupied as usual, should be rehabilitated before reoccupied or must be demolished [3]. Such a decision needs an accurate estimation of the residual properties of concrete, especially the mechanical strength to withstand the design loads. The physical and chemical actions that take place within the microstructure of concrete depend mainly on the temperature level reached and the fire exposure duration. Yet, the composition of the mixture, its porosity and the thermal properties of aggregate are also leading factors that determine the thermal resistance of concrete structures [3–6]. With the increase of temperature, several chemical and physical changes take place and affect the concrete strength owing to its heterogeneous state [7]. The first physical action of fire occurs at approximately 80 ◦C to 120 ◦C, where the contained free water in the concrete evaporates [7–9]. This action has a minor effect on concrete degradation, while the following action that usually occurs at temperatures higher than 300 ◦C and lower than 450 ◦C represents the starting point of the serious material degradation. This action is the dehydration of the C-S-H gel from the hydrated cement matrix [9–12]. The following actions depend not only on cement but also on the aggregate type [13–16]. The differences in thermal actions between the cement matrix and aggregate, due to the different thermal properties, result in breaking the bond at higher temperatures, which further weakens the concrete structure and deteriorates its residual strength [7,9]. Previous researchers showed that the tensile strength of concrete deteriorates at a faster rate compared to compressive strength [17,18]. Similarly, mechanical properties such as flexural strength, shear strength and modulus of elasticity showed significant deteriorations after exposure to 500 ◦C [19–23].

On the other hand, some parts of some structures are frequently subjected to the impact of falling objects or the lateral collision of moving vehicles, which are types of repeated accidental impact loads [24]. Other examples of repeated impacts are the offshore structures, where the waves of ocean water repeatedly subject these structures to hydraulic impacts. In hydraulic structures, such as stilling basins, the water acts as an impacting force on the downstream runway. Other examples of repeated impacts can be the forces subjected by airplane wheels on the airport runways [25–27]. The impact strength of concrete can be investigated using several techniques. However, the repeated impact test introduced by ACI 544-2R "Measurement of Properties of Fiber Reinforced Concrete" [28] is the simplest impact test and the only one that simulates the repeated impact case.

In recent years, several significant studies were conducted to evaluate the repeated impact strength of different concrete types using this testing technique. Mastali et al. [29] investigated the effect of the length and dosage of recycled carbon fiber reinforced polymer on the repeated impact performance of Self-Compacting Concrete (SCC). Ismail and Hassan [30] conducted experimental tests using the ACI 544-2R procedure to evaluate the impact resistance of SCC mixtures that include different contents of Steel Fibers (SF) and crumb rubber. The test results showed that the impact numbers increased by up to 30% and the impact ductility enhanced when crumb rubber was utilized, while the incorporation of 1% of SF significantly improved the retained impact numbers by more than 400%. The mono and dual effects of hooked-end and crimped SF on the ACI 544-2R impact resistance of SCC were investigated by Mahakavi and Chithra [31], where significant impact resistance improvement was reported when the two fiber types were hybridized. Jabir et al. [32] investigated the influence of single and hybrid micro SF and Polypropylene (PP) fibers on the impact resistance of ultra-high performance concrete. Abid et al. conducted ACI 544-2R [33] and flexural [34] repeated impact tests on SCC with micro SF contents of 0.5%, 0.75% and 1.0%. The results indicated that 1.0% of SF could increase the impact resistance by more than 800% compared to the reference plain specimens, while in another study [35], a percentage increase of approximately 1200% was recorded. Murali et al. [36–40] and others [41–43] conducted a series of experimental works that explored the repeated impact capabilities of multi-layered fibrous concrete. Double and triple layered concrete with preplaced aggregate and fibers with grouted cement paste were tested using

the ACI 544-2R. Works on this material [36,37,41] showed that using intermediate fibrous meshes can improve the impact resistance at cracking and failure stages. However, the most influential contribution to impact strength development was attributed to the steel fibers.

Compared to conventional concrete that have similar strength and fiber content, Engineered Cementitious Composites (ECCs) are a type of high-performance SCC concrete that possess extraordinary ductility with strain hardening and multiple cracking under tensile and flexural stresses. ECCs were first introduced by Li in 1993 [44] and used in several applications [45]. Since that time, numerous studies have been conducted to introduce different ECC mixtures with different fiber types and contents. Plenty of research is available in literature on the different mechanical properties of ECCs. However, research on ECC repeated impact behavior is rare. The performance of ECCs under repeated impact was experimentally investigated by Ismail et al. [46] using the ACI 544-2R technique. Different ECC mixtures were introduced using fixed contents of binder, water, sand and fiber. The results indicated that using 15% to 20% metakaolin with fly ash significantly enhanced the impact performance. Similarly, some studies that evaluate the performance and residual mechanical properties of different ECC mixtures after fire exposure are available in literature [47–50].

It is obvious from the introduced literature that very rare experimental works are available in literature on the repeated impact strength of ECCs. Similarly, there is a serious gap of knowledge about the residual impact strength of fibrous concrete after fire temperatures. To the best of the authors' knowledge, no previous research was conducted to study the residual repeated impact strength of ECCs after high temperature exposure. To fill this gap of knowledge, an experimental program was directed in this research to investigate the cracking and failure repeated impact performances and impact ductility of PP-based ECCs after exposure to high temperatures reaching 600 ◦C. Such type of research is required because both accidental fire and impact loading are expected along the lifespan of structures. Hence, the research outputs can be utilized to evaluate the residual material and structural response of structural members made of ECCs under such accidental cases.

#### **2. Materials and Methods**

#### *2.1. Mixtures and Materials*

The aim of this study is to evaluate the residual repeated impact performance of ECCs after exposure to elevated temperatures, which can be considered as a type of new concrete that includes no aggregate particles and a high content of fine cementitious and filler materials. The M45 is a typical ECC mixture introduced by leading researchers, which was the base and most widely used mixture with proven characteristics [44,45]. This mixture was used in this study but with PP fiber instead of the typical and much more expensive polyvinyl alcohol fiber (PVA). On the other hand, a normal strength conventional concrete mixture (NC) with an approximately comparative compressive strength was used for comparison purposes. The mix design proportions of both mixtures are detailed in Table 1.


**Table 1.** Material contents in the ECC and NC mixtures (kg/m<sup>3</sup> ).

A single type of Portland cement (Type 42.5) was used for both mixtures, while fly ash was used as a second cementitious material in the ECC mixture. The chemical composition and physical properties for both cement and fly ash are listed in Table 2. As preceded, the ECC mixture included no sand or gravel, where the filler of the mixture was composed of a single type of very fine silica sand with a grain size of 80 to 250 micrometer and a bulk density of 1500 kg/m<sup>3</sup> . On the other hand, local sand and crushed gravel from the central

region of Iraq were used as fine and coarse aggregates for the NC mixture. The grading of the sand and gravel are shown in Table 3, while the maximum size of the gravel particles was 10 mm. For the ECC mixture, a super plasticizer (SP) type ViscoCrete 5930-L from Sika® was used to assure the required workability due to the large amount of fine materials, while 2% by volume of PP fiber was used with the properties shown in Table 4.

**Table 2.** Properties of cement and fly ash.


**Table 3.** Grading of sand and gravel used for NC specimens.


**Table 4.** Properties of polypropylene fiber.


#### *2.2. Test Program and Heating Regime*

From each mixture and for each temperature level, six 150 mm diameter and 64 mm thick disk specimens were used to evaluate the repeated impact test under the free dropweight procedure of ACI 544-2R. On the other hand, six 100 mm cube specimens were used for a compressive strength test according to BS EN 12390-3: 2009 [51], while six beam specimens with 100 × 100 mm cross section and 400 mm length were tested under four-point bending test (300 mm span) for flexural strength according to BS EN 12390-5: 2009 [52]. All of the disk, cube and beam specimens were cured under the same standard conditions in temperature-controlled water tanks for 28 days.

After the curing period, the specimens were dried in the laboratory environment for 24 h. Previous researchers and trial tests conducted in this study showed that the heating of specimens without initial drying may lead to the explosive failure of some specimens at high temperatures. Therefore, all specimens were pre-dried using an electrical oven at a temperature of approximately 105 ◦C for 24 h. Afterwards, the specimens were heated using the electrical furnace shown in Figure 1a at a constant rate of approximately 4 ◦C/min to three levels of high temperatures of 200 ◦C, 400 ◦C and 600 ◦C. When the specified temperature level was reached, the temperature was kept constant for 60 min to assure the thermal saturation at this temperature. Finally, the furnace door was opened

and the specimens were left to cool slowly at the laboratory temperature until testing time. The heating regime of the three temperature levels is described in Figure 1b. In addition to the three groups of heated specimens, a fourth group was tested at room temperature without heating as a reference group.

**Figure 1.** Heating of test specimens; (**a**) the electrical furnace; (**b**) the heating regime curve.

#### *2.3. Repeated Drop-Weight Impact Test*

The impact response of materials and structures can be experimentally evaluated using different types of tests, among which is the drop-weight one. ACI 544-2R [28] addressed two types of drop-weight tests. The first is the instrumented drop-weight test which is the most commonly used technique to evaluate the impact response of structural members. This test is mostly used for reinforced beam and slab elements and requires expensive sensor instrumentation and data acquisition equipment. On the other hand, the alternative drop-weight impact test is a very simple one that is conducted on small size specimens and requires no instrumentation or any sophisticated measurement systems. This test requires that a drop weight of 4.54 kg is dropped repeatedly on the test specimen from a height of 457 mm until a surface crack becomes visible, then the repeated impacts are resumed until the fracture failure of the specimen. The numbers of the impacts at which the first crack and failure occur are recorded as the cracking impact number and failure impact number. The test is generally considered as a qualitative evaluation technique, which compares the impact resistance of different concrete mixtures based on their ability to absorb higher or lower cracking and failure impact numbers.

dropped by gravity on a steel ball, which rests on the center of the specimen's top surface. The standard test specimen is a cylindrical (disk) with a diameter of approximately 150 mm and a thickness of approximately 64 mm. The standard test is operated manually by hand-lifting the drop weight to the specified drop height and releasing it to be freely dropped by gravity on a steel ball, which rests on the center of the specimen's top surface. The steel ball is used as a load distribution point and is held in place using a special framing system that also holds the concrete disk specimen, as illustrated in Figure 2a. However, it was found in previous works [27,32] that the manual operation requires significant effort and is time consuming, especially because at least 6 replication specimens are required to assess the test records due to the high dispersion of this test's results [27]. Therefore, an automatic repeated loading machine was manufactured to apply the standard dropping weight from the standard dropping height with a better accuracy and much less effort. The manufactured machine was provided with a high accuracy digital camera to observe the surface cracking and failure in addition to a special isolation cabin to reduce the test noise. The manufactured repeated drop weight impact testing machine is shown in Figure 2b.

**Figure 2.** The drop-weight impact test; (**a**) schematic diagram of the test setup; (**b**) the automatic testing machine.

–

mens are required to assess the test records due to the high dispersion of this test's results

#### **3. Results of Control Tests**

#### *3.1. Compressive Strength*

The residual compressive strength–temperature relationship of the ECC tested cubes is shown in Figure 3, while Figure 4 shows that of the NC. It is clear in Figure 3 that the ECC strength reduced after exposure to 200 ◦C by approximately 22% compared to the reference unheated specimens, where the reference strength was 57.5 MPa, while it was 44.8 MPa after heating to 200 ◦C. A further decrease was recorded when the heating temperature was increased to 400 ◦C. However, this additional decrease was small compared to the initial one, where the residual strength percentages after exposure to 200 ◦C and 400 ◦C were approximately 78% and 70%, respectively. When the specimens were heated to 600 ◦C, a significant strength degradation was noticed with a residual compressive strength of 29.5 MPa, which means that the strength loss was approximately 49% compared to the strength of the unheated specimens. On the other hand, the percentage strength reduction of NC was less than that of the ECC after exposure to 200 ◦C and 400 ◦C. The residual compressive strength of the NC cubes after exposure to 200 ◦C and 400 ◦C was approximately 81% at both temperatures compared to the reference cubes as shown in Figure 4. However, the percentage residual compressive strength of the NC at 600 ◦C was approximately 50%, which was almost equal to that of the ECC (51.4%).

**Figure 3.** Residual compressive strength of ECC at different temperatures.

of pore size and number and the further volume changes' micro

**Figure 4.** Residual compressive strength of NC at different temperatures.

of pore size and number and the further volume changes' micro The denser microstructure of ECCs compared to NC is considered as the main cause of the further strength reduction between 200 ◦C and 400 ◦C. ECCs comprise a much larger amount of very fine binder, fine silica sand, no coarse aggregate and lower water/cementitious material content, which in turn lowers the porosity of the ECC compared to the NC. The evaporation of the free pore water below 200 ◦C induces a pore pressure inside the microstructure. The dissipation of this pressure in the NC specimens due to the higher porosity relieves the internal thermal stresses, while these stresses are higher in the ECC due to the denser microstructure. As a result, the ECC suffered higher compressive strength losses at 200 ◦C and 400 ◦C. Previous researchers [53] reported that the total volume of the 0.1 micrometer and larger pores in the ECC reduced after exposure to 400 ◦C, which is attributed to the pozzolanic reaction of the unhydrated fly ash and other cementitious materials. Such a reaction would induce unfavorable volume changes due to the production of more C-S-H gel, which results in microstructural cracking leading to further strength degradation. The dehydration of hydrated products after exposure to temperatures higher than 400 ◦C is the main cause of the steep strength reduction at 600 ◦C, where this process leads to the degradation of the microstructure due to the increase of pore size and number and the further volume changes' micro-cracking. Sahmaran et al. [47] reported a significant increase in the volume and size of the pores of the ECC after exposure to 600 ◦C, where the porosity increased by 9% after exposure to 600 ◦C, which is large enough compared to 5% after exposure to 400 ◦C, while the pore size increased by at least 300% after 600 ◦C exposure.

#### *3.2. Flexural Strength*

As shown in Figure 5, the flexural strength of the ECC followed a continuous decrease behavior with temperature up to 600 ◦C. The reference flexural strength of the ECC at room temperature was 6.94 MPa, while it reduced to 5.75 MPa, 4.32 MPa and 2.31 MPa after exposure to 200 ◦C, 400 ◦C and 600 ◦C, respectively. This means that the strength respective reductions at these temperatures were approximately 17%, 38% and 67%. Similarly, the NC showed a continuous steep decrease in flexural strength with temperature increase as shown in Figure 6. The residual flexural strength records of the NC after heating to 200 ◦C, 400 ◦C and 600 ◦C were 2.87 MPa, 2.16 MPa and 0.32 MPa, while the reference unheated specimens recorded a flexural strength of 3.70 MPa. Hence, the percentage reductions were approximately 22%, 42% and 91% at 200 ◦C, 400 ◦C and 600 ◦C, respectively.

**Figure 5.** Residual flexural strength of ECC at different temperatures.

**Figure 6.** Residual flexural strength of NC at different temperatures.

in the specimens' appearance were noticed after high temperature exposure. However, i – crack's opposite sides, resulting in a more gradual and ductile fa The continuous decrease in the flexural strength after high temperature exposure is generally attributed to the volumetric changes in the cement matrix due to vapor movements beyond 100 ◦C and the bond loss between binder and filler after 400 ◦C due to their different thermal properties. In addition, most of the degradation at higher temperatures is attributed to the chemical reactions after 400 ◦C (dehydration of C-S-H) and the increased porosity as discussed in the previous section. As the flexural strength depends on the capability of concrete to withstand tensile stresses, the initial flexural strength was apparently higher for the ECC owing to the crack bridging activity of PP fibers, in addition to the higher content of cementitious materials. However, this bridging activity diminished after exposure to temperatures higher than 200 ◦C due to the melting of PP fibers. The better performance of the ECC at high temperatures compared to the NC might be attributed to the finer mixture constituents and the absence of coarse aggregate in the ECC, which minimized the effect of bond degradation. Wang et al. [54] showed that the residual flexural strength of PVA-based ECC after exposure to 400 ◦C was approximately 58% of the unheated strength, which is quite comparable to the obtained result in this study, while Yu et al. [55] reported that PVA-based ECC exhibited flexural strength reductions of more than 50% and more than 40% after exposure to temperatures of 400 ◦C and 600 ◦C, respectively.

#### **4. Results of Repeated Impact Test**

#### *4.1. Description of Heated Specimens*

Figure 7 shows the appearance of the external surfaces of a reference impact disk specimen and others heated to 200 ◦C, 400 ◦C and 600 ◦C before testing. No significant

**b**) 2

changes in the specimens' appearance were noticed after high temperature exposure. However, it was observed that the gray color became lighter after 200 ◦C and small yellow areas were noticed on the surface of specimens exposed to 600 ◦C. This slight color change might be due to the decomposition of C-S-H gel particles [56–58]. It should also be noticed that PP fibers cannot sustain high temperatures where its melting point is less than 200 ◦C. As shown in Figure 8a, the presence of PP fibers had a significant impact in bridging the crack's opposite sides, resulting in a more gradual and ductile failure of the reference unheated specimens. On the other hand, the complete melting of fibers after exposure to 400 ◦C and higher eliminated this effect and created a more porous media. The channels left after fiber melting would connect and produce continuous porous networks, which have a positive effect by relieving the internal stresses due to the vapor pressure dissipation. On the other hand, these channels may have a negative effect by making the media more porous and hence more brittle under loads. Figure 8b shows that after exposure to 600 ◦C, the vaporization of PP fibers changed the internal color of the specimen to a dark gray and left a very porous structure behind. in the specimens' appearance were noticed after high temperature exposure. However, i – crack's opposite sides, resulting in a more gradual and ductile fa

(**a**) R (**b**) 200 °C

**Figure 7.** Impact test specimens subjected to different temperatures.

**Figure 8.** Physical appearance of PP fibers in the impact specimens before and after heating.

#### *4.2. Cracking and Failure Impact Numbers*

The recorded cracking numbers (Ncr) of the ECC and NC are shown in Figure 9 at different levels of high temperatures, while the results of failure numbers (Nf) are shown in Figure 10. It is worthy to mention that the ACI 542-2R test is known for the high despersion of test results, where the Coefficient of Variation (COV) of the Ncr records of the ECC was in the range of 42% to 68.8%, while the COV of the recorded Nf results of the ECC specimens was in the range of 30.9% to 61.8%.

**Figure 9.** Residual cracking impact numbers of ECC and NC at different temperatures; (**a**) cracking number; (**b**) residual ratio of cracking number.

**Figure 10.** Residual failure impact numbers of ECC and NC at different temperatures; (**a**) failure number; (**b**) residual ratio of failure number.

Figure 9 shows that the reference unheated cracking number of the NC was higher than that of the ECC, which is attributed to the presence of gravel in the NC that enabled it to absorb a higher initial number of impacts before cracking. However, after high temperature exposure, the NC specimens showed much weaker response and deteriorated at much higher rate compared to the corresponding ECC specimens as shown in Figure 9a,b. The unheated Ncr of the ECC and NC were 43.3 and 55, respectively, noting that each impact number represents the average of six specimen records. On the other hand, the residual ECC cracking numbers were 41.5, 19.5 and 8.8 after exposure to 200 ◦C, 400 ◦C and 600 ◦C, respectively, while those of the NC specimens were 14.2, 3 and 1, respectively. The results reveal a steep drop in the cracking impact numbers of the NC, where the percentage residual Ncr values were only 25.8%, 5.5% and 1.8%, respectively, compared to the reference unheated number as shown in Figure 9b. On the other hand, the ECC showed an insignificant decrease (less than 5%) after exposure to 200 ◦C, while the percentage residual Ncr values were 45% and 20.4% after exposure to 400 ◦C and 600 ◦C, respectively. The rapid decrease of the Ncr of the NC is attributed to the discussed physical and chemical changes that occur after exposure to high temperatures, especially the dehydration of C-S-H, which deteriorates the cement matrix, in addition to the different thermal movements of cement paste and aggregate. Consequently, the internal structure becomes more and more brittle as the temperature increases, which leads to the loss of impact energy absorption capacity and hence to rapid cracking. On the other hand, the higher cementitious materials content, the finer matrix and the absence of aggregate reduced these effects and enabled the ECC specimen to continue withstanding more impacts before cracking. It should be noticed that although the melting point of PP fibers is less than 200 ◦C, a significant amount of these fibers still existed in the specimens heated to 200 ◦C. These fibers helped maintain a significant impact number before cracking, which is approximately equal to that of the unheated specimens (95.8%). Aslani et al. [59] reported that PVA fibers did not melt completely after exposure to 300 ◦C, which is higher than the approximate melting point of PVA (200 ◦C to 230 ◦C).

ECCs are known for their high ability to withstand plastic deformation after cracking under tensile and flexural loads, which is attributed to their unique microstructure with high content of binder and fine filler in addition to the potential of fibers to withstand high tensile stresses across the cracks. These characteristics enabled the ECC specimens to absorb significantly higher energy compared to NC after cracking. The test results of this study showed that this potential is also valid under repeated impact loads. As shown in Figure 10, the failure impact number (Nf) of the unheated ECC specimens jumped to a very high limit compared to its corresponding Ncr, while that of NC was comparable to its cracking number, which duplicated the difference of Nf between the ECC and NC several times although the Ncr of the NC was higher than that of the ECC. The Nf of the unheated ECC was 259.3, while that of the NC was only 57.2. This means that the Nf of the NC was approximately equal to its Ncr with only 2.2 higher impacts, while the ECC sustained 216 more impacts after cracking.

After exposure to 200 ◦C, the NC specimens lost approximately 73% of their initial failure impact performance and retained only 15.2 impacts at failure. Oppositely, the ECC specimens kept approximately the same failure strength of the unheated specimens due to the same reasons discussed above. As shown in Figure 10b, the residual Nf of the ECC after exposure to 200 ◦C was 99% of the corresponding unheated Nf with 256.7 impacts. As discussed previously, the PP fibers did not melt completely at 200 ◦C, which means that the fiber bridging activity was still partially effective after cracking. The hydration of the unhydrated products at this temperature might be another reason that enabled the specimens to sustain high impact numbers before cracking. On the other hand, as temperature increased beyond 200 ◦C, the microstructure of the ECC deteriorated steeply after the complete melting and vaporization of the PP fibers (around 340 ◦C [60]) and the decomposition of C-S-H gel, which resulted in a weak microstructure. Therefore, the impact strength deteriorated sharply after exposure to 400 ◦C and 600 ◦C. As shown in Figure 10b, the percentage residuals of the Nf after exposure to these temperatures were only 9.2% and 3.8%, respectively.

#### *4.3. Failure Patterns of Impact Specimens*

The post-failure appearance of a reference ECC specimen and others heated to different high temperatures after repeated impact loading are shown in Figure 11. It is clear in Figure 11a that the central loading area of the top surface of the reference specimen was fractured due to the damage. This fracture zone occurred under the effect of the repeated concentrated compressive stresses from the steel ball, which reflects the ability of the

material to absorb significant impact energy under the concentrated impact loading. After the fracture of the surface layer, the PP fibers kept bridging the internal micro-cracks where the compressive impacts try to split the cylinder and hence induce internal tensile stresses, see Figure 8a. However, the continuous impacting could finally break the fibers or their bond with the surrounding media resulting in a progressive crack widening and propagation. Hence, the surface cracks become visible. As shown in Figure 11a, the reference specimens exhibited a ductile failure behavior with central fracture zone and multi-surface cracking.

(**a**) R (**b**) 200 °C

(**c**) 400 °C (**d**) 600 °C

**Figure 11.** Failure patterns of tested impact specimens heated to different temperatures.

Referring to the impact response of the ECC specimens after exposure to 200 ◦C, the failure pattern at this temperature was similar to that of the reference unheated specimens, but with a lower number of standing fibers across the mouth of the main crack. It should also be noticed that the other minor cracks were wider at this temperature (Figure 11b) compared to those of the specimens, which discloses the lower ductility and higher brittleness of the heated specimens. As previously disclosed, the heating to 400 ◦C and 600 ◦C caused serious damage to the microstructure of the ECC and vaporized the reinforcing elements (PP fibers), which was approved by the brittle and sudden failure of the specimens to two, three or four pieces with wide cracks. This failure was not associated with central fracturing as in the case of the reference and 200 ◦C specimens, where the thermally weakened structure could not absorb significant concentrated impacts, as shown in Figure 11c,d.

#### **5. Strength Correlation with Temperature**

In some cases, it is required to evaluate the residual strength of a material after exposure to a specific temperature. If sufficient experimental data are not available, extrapolation from other existing data may be considered satisfactory for a quick primary evaluation. Despite the limited number of points for each fit, simplified correlations were introduced, as shown in Figure 12, to describe the relation of the strength and impact numbers of the PP-based ECC after exposure to high temperatures. Figure 12a shows that the relations of both compressive strength and flexural strength with temperature can be represented using linear fits with good determination coefficients (R<sup>2</sup> ) of 0.96 and 0.99, respectively. Referring to Figure 12c, it can be said that a multilinear relation would better describe the reduction of compressive strength with temperature. However, a determination coefficient of 0.96 is good enough to accept the simpler linear correlation.

‐ ‐ ‐ ‐ The impact numbers showed a weaker linear correlation degree with temperature than those of compressive strength and flexural strength. As shown in Figure 12b, the linear relations of Ncr and Nf with temperature underestimate the retained impact numbers at 200 ◦C, while that of Nf overestimates the experimental failure impact number recorded at 400 ◦C. The deviations from the experimental records at these temperatures impacted the degree of the linear correlation, especially for Nf, where the R<sup>2</sup> of the linear correlation was 0.84, which is the lowest among the obtained ones. To avoid such a low degree of correlation, nonlinear correlations were tried and the exponential one was found to give a coefficient of determination of 0.9, which is quite acceptable as an indication of a good correlation. As shown in Figure 12c, the exponential correlations could acceptably estimate the degradation of Ncr and Nf after exposure to the highest temperatures (400 ◦C and

‐ ‐

‐ ‐ ‐

‐ ‐ 600 ◦C). However, these correlations significantly underestimated the residual impact numbers after exposure to 200 ◦C.

#### **6. Conclusions**

Compressive, flexural and repeated impact tests were conducted in this study to evaluate the residual strength of PP fiber-based ECCs after exposure to high temperatures up to 600 ◦C. Based on the results obtained from the experimental work of this study, the following are the most important conclusions:

1-The compressive strength of the ECC decreased with temperature increase. However, the residual strength at 400 ◦C was close to that at 200 ◦C, while exposure to 600 ◦C led to a significant strength reduction. The percentage residual compressive strengths of the tested ECC cubes after exposure to 200 ◦C, 400 ◦C and 600 ◦C were approximately 78%, 70% and 51%, respectively. The reason for the strength deterioration after 400 ◦C is attributed to the chemical and physical changes within the material microstructure due to the temperature exposure, which include the decomposition of C-S-H gel and the increase of porosity owing to the vaporization of PP fibers. The linear correlation could effectively describe the degradation of compressive strength after high temperature exposure with an R<sup>2</sup> of 0.96.

2-The flexural strength of the ECC showed a clear continuous reduction with temperature compared to that of compressive strength and higher percentage reductions at 400 ◦C and 600 ◦C. Therefore, the linear correlation with temperature was the most accurate one among the conducted tests with an R<sup>2</sup> of 0.99. The residual flexural strengths were reduced to approximately 62 and 33% after heating to 400 ◦C and 600 ◦C, respectively.

3-The ECC specimens exhibited minor reductions in the cracking number (Ncr) after exposure to 200 ◦C with a residual percentage of approximately 96%. The reduction in Ncr was much higher after exposure to the higher temperatures. However, the deterioration of normal concrete (NC) was much faster. ECCs retained percentage residual Ncr values of approximately 45% and 20% after exposure to 400 ◦C and 600 ◦C, respectively, while the corresponding percentages of NC were approximately 5% and 2%. The much higher binder content, finer matrix and the absence of aggregate enabled the heated ECC specimen to continue absorbing higher impacts till cracking compared to NC.

4-The failure impact number of the unheated ECC specimens jumped several times higher than the corresponding Ncr, which assured the ability of the dense and fine microstructure of the ECCs, with the help of the PP-fibers crack bridging elements, to amplify the capacity impact energy absorption at failure. The retained Nf was 259.3, which was approximately 4.5 times that of NC although of the higher Ncr of NC. After exposure to 200 ◦C, the ECC retained almost the same unheated Nf number (99%), while NC retained only 27% of its unheated failure number. Oppositely, both ECC and NC sharply lost their impact resistances after exposure to 400 ◦Cand 600 ◦C with percentage residual Nf values of less than 10%, and 4%, respectively.

5-The linear correlation was found suitable to describe the reduction of Ncr with temperature with a good R<sup>2</sup> of 0.93. However, such correlation noticeably underestimated the recorded Nf at 200 ◦C and overestimated that at 400 ◦C, which decreased its R<sup>2</sup> to 0.84. On the other hand, the exponential relation was found to better describe the deterioration of Nf after high temperature exposure, where R<sup>2</sup> was 0.9.

**Author Contributions:** Conceptualization, S.R.A.; methodology, R.A.A.-A. and S.R.A.; validation, S.R.A. and M.Ö.; formal analysis, S.R.A. and R.A.A.-A.; resources, R.A.A.-A.; data curation, S.R.A. and R.A.A.-A.; writing—original draft preparation, S.R.A. and R.A.A.-A.; writing—review and editing, S.R.A. and M.Ö.; visualization, S.R.A. and R.A.A.-A.; supervision, S.R.A. and M.Ö.; project administration, S.R.A. and M.Ö. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not Applicable.

**Informed Consent Statement:** Not Applicable.

**Data Availability Statement:** Data are available upon request from the corresponding author.

**Acknowledgments:** The authors acknowledge the support from Al-Sharq Lab., Kut, Wasit, Iraq and Ahmad A. Abbas.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Mohamed Monir A. Alhadid and Maged A. Youssef \***

Department of Civil and Environmental Engineering, Western University, London, ON N6A 5B9, Canada; majjanal@uwo.ca

**\*** Correspondence: youssef@uwo.ca

**Abstract:** A simplified procedure to predict the residual axial capacity and stiffness of both rectangular and circular reinforced concrete (RC) columns after exposure to a standard fire provides the means to replace the current descriptive methods. The availability of such a procedure during the design phase provides engineers with the flexibility to come up with better designs that ensure safety. In this paper, finite difference heat transfer and sectional analysis models are combined to determine the axial behavior of RC columns with various end-restraint conditions at different standard fire durations. The influence of cooling phase on temperature distribution and residual mechanical properties is considered in the analysis. The ability of the model to predict the axial behavior of the damaged columns is validated in view of related experimental studies and shown to be in very good agreement. A parametric study is then conducted to assess the axial performance of fire-damaged RC columns. A procedure is proposed to determine the residual strength and stiffness of fire-damaged RC columns in typical frame structures.

**Keywords:** reinforced concrete; columns; standard fire; cooling phase; axial capacity; temperaturestress history

#### **1. Introduction**

Reinforced concrete (RC) structures are widely used in construction due to their outstanding structural performance and design flexibility [1]. The behavior of RC members at ambient conditions is addressed by various building codes and standards [2–4]. However, when exposed to elevated temperatures, the capacity and deformation of such members change due to material degradation, residual strains, and stress redistribution [1,5,6]. In addition, the temperature–load history and the interaction between mechanical and thermal stresses significantly affect the residual properties of the members [1,7,8].

The structural integrity and mechanical properties of most fire-exposed concrete members are either fully or partially restored after the fire incident. Many design codes and standards [9–12] adopt a prescriptive approach through providing data related to the anticipated fire resistance of various RC members based on their geometrical properties and fire exposure conditions. This approach is easy to implement but usually results in bigger sections than what is required to support the loads. The prescriptive approach also overlooks the influence of temperature–load history despite its important role in determining the residual performance of the members. In practice, a preliminary assessment of the damaged members is performed immediately after the structure is exposed to elevated temperatures [13]. This includes visual inspection, hammer tapping, determination of fire propagation route and residual strength of concrete, cracking and spalling schemes, color changes, and smoke deposits to identify the fire duration and maximum temperatures reached [14]. After that, the structure is evaluated according to the relevant design code based on the extent of damage and the affordability of the required work. Load-bearing members, such as columns, should maintain their structural integrity to sustain the applied load without failure or excessive deflections.

**Citation:** Alhadid, M.M.A.; Youssef, M.A. Residual Axial Behavior of Restrained Reinforced Concrete Columns Damaged by a Standard Fire. *Fire* **2022**, *5*, 42. https:// doi.org/10.3390/fire5020042

Academic Editor: Wojciech W˛egrzy ´nski

Received: 24 February 2022 Accepted: 17 March 2022 Published: 23 March 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

This study is an attempt to propose an analytical procedure to supplement the in situ preliminary assessment after a fire incident in RC structures considering standard fire. A model utilizing both heat transfer analysis and sectional analysis is developed to evaluate the residual axial behavior of rectangular and circular RC columns. Temperature–load history is explicitly considered in the analysis. The various strain components developed during and after fire are calculated and their influence on changing the residual performance of the damaged members under various restraining conditions is evaluated. The validity of the proposed model is assessed in view of relevant experimental results obtained from the literature. The validated model is then utilized to perform a parametric study aiming at investigating the influence of mechanical properties, cross-sectional dimensions, fire exposure and support conditions on the residual performance of RC columns. A simplified procedure is then proposed to predict the residual axial capacity and stiffness of RC columns in typical frame structures. The outcomes of the current study provide a solid basis for a more comprehensive work that accounts for other fire types and exposure conditions.

The determination of the residual axial capacity of RC columns subjected to elevated temperatures is not practical in design offices due to the complexity associated with performing comprehensive thermal and structural analyses. The proposed simplified method allows engineers to utilize the commercially available structural analysis software to predict the residual axial capacity and deformation behavior of fire-exposed structures. This can be performed by considering the residual axial stiffness as an input in the definition of the mechanical properties of the affected members to account for the deterioration they exhibited due to elevated temperatures. The internal forces in all the members can then be obtained due to the load redistribution triggered by the fire scenario. The capability of the structural members to resist the applied loads is determined in view of their residual capacity. The residual axial properties used in performing the structural analysis study are obtained from the proposed models in the current article.

#### **2. Proposed Analytical Approach**

Assessment of the post-fire behavior of RC columns in typical frame structures requires the consideration of not only the residual mechanical properties of the composing materials but also the temperature–load interaction before and during fire. Figure 1 illustrates the influence of heating and loading history on the total strains (*εt*) induced in concrete. Path 1 shows the case where the column supports a load that causes a mechanical strain (*εm*)<sup>1</sup> before heat exposure. By heating the column, a combination of thermal and transient strains (*εth*)<sup>1</sup> is induced. On the other hand, path 2 shows the development of total strains under a successive application of temperature and load. In this case, the column experiences thermal strains (*εth*)<sup>2</sup> followed by mechanical strains (*εm*)<sup>2</sup> due to the loads applied on the fire-damaged member. Transient strains are not considered as the column is unloaded during heating. Although the column is supporting the same load and is exposed to the same maximum temperature in both cases, the total strain differs significantly. In real structures, the total strain can be somewhere in between the two previously mentioned extreme cases. Since the free thermal strain is partially irrecoverable and the transient strain is irreversible [7,15], detailed examination of the actual load–temperature path must be considered in the analysis. Guo and Shi [1] experimentally demonstrated the variation in the deformation behaviors of RC columns when subjected to different heating–loading paths.

The analytical approach performed in this study encompasses three main stages that describe the structural variations in the exposed member throughout the heating–cooling cycle. Firstly, the structural performance of the intact member is determined in terms of its capacity and stiffness considering the relevant material models at ambient conditions. The obtained structural characteristics act as a basis to calculate the initial axial load level (*λ*) and to determine the extent of deterioration in the member after exposure to fire. The second stage involves thermal and structural analyses of the exposed member during the heating and cooling cycles. Heat transfer analysis is carried out using the finite difference

method to determine the maximum temperature distribution within the member based on concrete thermal and physical properties. In Figure 2, the residual properties of the member at the final stage (point 2) are highly dependent on the temperature–load path followed. Therefore, at each time increment, the change in the applied load level (∆*σ*) associated with the restraint conditions is considered. Both thermal and transient strains are calculated at each time increment, as represented by the step function shown in Figure 2. The residual capacity of the member during fire is calculated based on the relevant material models to check if failure occurs during fire. The third analysis stage commences after the member is completely cooled down to room temperature. In this stage, sectional analysis is carried out to determine the residual capacity and stiffness of the fire-damaged member in view of the maximum temperature reached and residual strain distribution. The analysis is performed by applying uniform strain increments until failure occurs considering the post-fire mechanical properties and material models. *λ*

**Figure 1.** Influence of temperature–stress interaction on the concrete strains.

**Figure 2.** Potential temperature–stress paths between initial and final conditions of the fireexposed members.

*Δσ*

*Δσ*

The current study focuses on the axial behavior of rectangular and circular RC members exposed to fire from all sides. The restraint condition is determined by performing structural analysis of the entire frame, Figure 3a, with the aid of a suitable commercially available software. The first iteration is performed considering the mechanical properties of the section at ambient conditions. At any specific time during fire, the columns' axial capacity and stiffness are reduced as a function of the temperature distribution within the section. The fire-exposed column can be isolated as shown in Figure 3b. A pin support is assigned to one end of the column, while the other end is attached to a roller support and a spring with an axial stiffness (*k<sup>δ</sup>* ) that represents the axial constraints provided by the adjacent frame members. The value of *k<sup>δ</sup>* can be obtained based on structural analysis, as will be discussed later in Section 11 of this paper. Springs act in resisting the columns' expansion but not contraction. When the column expands, the magnitude of the axial load acting on the column encompasses both the initial applied load (*P<sup>i</sup>* ) and the restraining force caused by thermal expansion. The axial stiffness (*EA*) of the columns varies at each time step during fire and is considered in the calculation of the restraining force. The mutual dependency is considered in the proposed model, as discussed in the subsequent sections. *δ δ*

(**a**) Typical RC frame exposed to fire (**b**) Idealized column

**Figure 3.** Isolation of a fire-exposed column in a typical RC frame.

The proposed analysis of the fire-damaged RC members is carried out based on the following assumptions:


#### **3. Definition of Cross-Sections**

The residual axial capacity and stiffness of fire-exposed RC rectangular and circular columns subjected to standard fire from all sides are considered in the analysis. The geometrical properties and reinforcement distribution of a typical cross-section are defined in Figures 4a and 5a for rectangular and circular sections, respectively. Rectangular sections are defined in terms of section width (*b*), section height (*h*), steel reinforcement ratio (*ρ*), top *ρ*

steel reinforcement (*Ast*) and bottom steel reinforcement (*Asb*), whereas circular columns are defined in terms of cross-sectional diameter (*D*), steel reinforcement ratio (*ρ*) where steel reinforcement (*As*) is assumed to be uniformly distributed along the circumference. Table 1 details the mechanical and geometrical properties of the selected rectangular and circular sections discussed in this paper.

*ρ ρ*

*ρ*

**Figure 5.** Geometry and meshing of circular sections.

∆ = ൞

−4.167 ൬3 −

− = 750 ൣ1 − ൫ ିଷ.ଽହହଷ √௧ <sup>൯</sup>

௧

−10.417 , < 30 min

−4.167 , ≥ 120 min

൧ + 170.41√

௧

<sup>60</sup> ൰ , 30 min ≤ < 120 min


**Table 1.** Properties of the considered rectangular and circular column sections.

#### **4. Thermal Analysis**

Temperature distribution at any section along the member is determined based on the finite difference method described by Lie [16]. The physical and thermal properties of both concrete and steel are provided by Lie [16]. For each time increment, the temperature distribution within the section is obtained by solving the heat balance equations [16]. In the current study, the columns are exposed to an ASTM E119 [17] standard fire along their perimeter during the heating phase, as approximated by Equation (1).

$$T\_f - T\_o = 750 \left[ 1 - e^{(-3.79553 \sqrt{t})} \right] + 170.41 \sqrt{t} \tag{1}$$

where *T<sup>f</sup>* is the fire temperature (◦C), *T<sup>o</sup>* is the room temperature (◦C) and *t* is the time after the start of the fire (hr). During the cooling phase, the rate of decrease in temperature per minute is calculated according to the ISO 834 [18] specifications as provided in Equation (2) in terms of fire duration at the end of the heating phase (*thot*).

$$
\Delta T = \begin{cases}
\end{cases}
\tag{2}
$$

Concrete thermal properties are assumed to be irreversible and maintain a constant value corresponding to the maximum temperature reached [1,15]. A distinction in the meshing procedure between rectangular and circular column sections is illustrated in Figures 4b and 5b, respectively.

#### *4.1. Rectangular Sections*

The analysis procedure begins by dividing the cross section into M × N 45◦ inclined square elements, as shown in Figure 4b. The point at the center of each internal element or on the hypotenuse of each boundary element represents the temperature of the entire element. Steel bars are considered as perfect conductors due to their high thermal conductivity, and their temperature is assumed to be identical to the adjacent concrete elements. Heat energy is transferred from the outer elements toward the concrete core, causing a subsequent increase in temperature depending on concrete thermal conductivity and moisture content. The influence of moisture is considered by assuming that when an element reaches a temperature of 100 ◦C, all the transferred heat causes the evaporation

of water particles instead of raising the element's temperature. Heat transfer equations between the elements throughout the cross-section are given by Lie [16].

Having determined the temperature distribution within the cross-section, the section is divided into multiple horizontal layers, each having a thickness of ∆ℓ sin(45◦ ), as shown in Figure 4c. Average temperature is then calculated in each layer considering two methods that result in different temperature distribution along the cross-section. In the first one, the temperature of each horizontal layer is calculated as the algebraic average temperature of the square elements composing it. The other calculation procedure is performed by first calculating the residual compressive strength of each square element, and then evaluating the temperature, which would result in the same average compressive strength in that layer. The first temperature distribution is utilized to calculate thermal and transient strains, whereas the second one is used in calculating the residual strength of each layer. The temperature of the steel layer is assumed to be similar to the temperature of the square mesh elements within which they are located. A similar procedure was performed and validated by El-Fitiany and Youssef [6].

#### *4.2. Circular Sections*

To determine the temperature within the circular cross-section along the RC columns, the area is first divided into *M* concentric layers as shown in Figure 5b. The change in temperature (*T*) in each circular layer is derived by solving the heat balance equations at each time increment, assuming that the column is exposed to heat along its circumference, as described by Lie [16]. The influence of steel bars and moisture contents is considered in the analysis in a similar manner to the rectangular sections.

In this study, a method is proposed and validated to transform the circular layers into equivalent horizontal layers that can be utilized in the sectional analysis procedure. The procedure commences by dividing the semi-circular section into *M* horizontal layers (*I*), each corresponding to a unique circular layer (*J*), as indicated in Figure 5c. The upper and lower boundaries of any horizontal layer (*I*) are taken as the tangents to the two circular layers denoted by (*J* = *I*) and (*J* = *I* − 1), respectively. The intersection between the horizontal and circular layers produces elementary layers whose temperatures represent the temperature of the circular element they are located in. The area (*A*) of each elementary layer is derived in terms of the distance (*r*) from the center of the circular cross-section to each layer, as given in Equation (3).

$$A\_{I,I} = \begin{cases} \frac{\pi \frac{r\_I^2}{2}}{2} & \text{, } I = J = 1\\\ r\_I^2 \times \frac{2 \cos^{-1} \left(\frac{r\_{I-1}}{r\_I}\right) - \sin \left[2 \cos^{-1} \left(\frac{r\_{I-1}}{r\_I}\right)\right]}{2} & \text{, } I = J\\\ \frac{\pi \frac{r\_I^2}{2}}{2} - r\_I^2 \times \frac{2 \cos^{-1} \left(\frac{r\_I}{r\_I}\right) - \sin \left[2 \cos^{-1} \left(\frac{r\_I}{r\_I}\right)\right]}{2} - \sum\_{i,1}^{I,j} A\_{i,j} & \text{, } I \neq J \end{cases} \tag{3}$$

The temperature in each layer is calculated twice, similar to the procedure performed in rectangular sections. However, in the first case, the weighted average is calculated for each layer instead of calculating the normal average. This requires the determination of the area and temperature of each small element composing the horizontal layer. In the second case, the average temperature that would result in the same weighted average of residual compressive strength is determined. The temperature of each steel layer is taken as the maximum temperature reached at a distance equal to the provided concrete cover since all bars are uniformly distributed parallel to the circumference.

For both rectangular and circular columns, the temperature distribution within the section varies with the thermal properties of concrete and the cross-sectional dimensions. Figure 6 illustrates the change in temperature at different points along the mid-width of sections R3 and C3, whose characteristics are detailed in Table 1. The location of each point is defined as the distance from the face of the column in terms of section height (*h*) for rectangular sections and radius (*r*) for circular sections. Two main observations can be

drawn from these figures. Firstly, curves representing the points further away from the surface show a continuous increase in temperature after the end of heating. This causes the maximum temperature in the interior elements to be reached during the cooling phase, indicating that heat flow propagates not only to the atmosphere, but also to the inner, colder portions of the member. The second observation shows that cooling continues for a considerable amount of time before heat flow starts to take one direction only toward the atmosphere. A distinction between the rectangular and circular sections is detected in terms of response to temperature variation. In the aforementioned two sections, the concrete in column C3 located at a distance of up to (0.5 *r*) responds faster to the increase in temperature than that in rectangular sections located at the same distance. However, at a greater depth within the section, temperature variation becomes less pronounced in the circular section compared to its rectangular counterpart. This change in behavior is attributed to the more concrete area acting as a protecting cover for points closer to the core in section C3 compared to section R3.

(**a**) Rectangular section (R3) (**b**) Circular section (C3)

**Figure 6.** Temperature variation with time at different points along the cross-section.

0

0.0 2.5 5.0 7.5 10.0

(cover)

707

548

(0.25 /2)

(0.50 /2)

454 427

(0.75 /2)

**Time from fire initiation (hr)**

250

500

**Temperature, (**

**oC)**

750

1000

1250

**Figure 7.** Temperature distribution within the rectangular cross-section of column (R3) at different time increments.

0

0.0 2.5 5.0 7.5 10.0

(cover)

(0.25 )

(0.50 ) (0.75 )

435 406

**Time from fire initiation (hr)**

250

500

**Temperature, (**

**oC)**

750

762

575

1000

1250

**Figure 8.** Temperature distribution within the circular cross-section of column (C3) at different time increments.

#### **5. Material Models and Strain Components**

் ᇱ *ε* The general form of the Tsai [19] model is adopted in this study to represent the compressive stress–strain relationship of concrete at all stages. During fire, the reduced compressive strength due to fire (*f* ′ *cT*) proposed by Hertz [15] is used, whereas concrete strain at peak stress at elevated temperatures (*εoT*) is determined by the Terro [20] formula. The post-fire mechanical properties are calculated based on the expressions by Chang et al. [21].

Regarding steel, the constitutive model used by Karthik and Mander [22] is adopted for both ambient and post-fire conditions as it conveniently combines the initial elastic response, yield plateau and strain hardening stages. At elevated temperatures, the Lie [23] model is used as it implicitly includes the reduction in yield strength due to fire.

*ε ε<sup>σ</sup> ε ε ε* Total strain in concrete (*εt*) is calculated as the summation of stress-related strain (*εσ*), free thermal strain (*εth*), creep strain (*εcr*), and transient strain (*εtr*). The tendency of the structural members to deform due to external applied loads is described in terms of the

*ε*

*ε*

*ε*

−

*ε*

stress-related strain component. Free thermal strain of both concrete and steel bars is determined from Eurocode [4]-proposed expressions. The residual free thermal strain (*εthR*) represents the irreversible part of the free expansion that occurred during fire. After a complete heating–cooling cycle, thermal strain is restored with a rate of 8 <sup>×</sup> <sup>10</sup>−6/ ◦C from the maximum temperature reached [1], while *εthR* for steel is set to zero. If the member is initially loaded or restrained, then transient strain is generated in concrete and maintains its maximum values after cooling [1]. The empirical model proposed by Terro [20] is adopted to calculate the transient creep strain as referred to by load-induced thermal strain (*εLITS*). Regarding steel bars, the residual thermal strain is brought back to zero at the end of the cooling phase. Both transient and creep strain are not applicable for steel during and after fire. Detailed descriptions of the material models and strain components during fire exposure are provided by Youssef and Moftah [5].

#### **6. Strength Analysis**

An iterative sectional analysis procedure is carried out to determine the residual *P*-*ε* behavior of the fire-damaged RC columns. The residual properties are determined in view of the temperature distribution obtained from thermal analysis. At every loading step, the axial strain is increased incrementally until reaching the total applied axial load. The kinematic and compatibility conditions are considered in view of the corresponding residual mechanical properties and stress–strain relationships of both concrete and steel. The strength analysis is performed by dividing the cross-section into multiple horizontal layers, as shown in Figures 4c and 5d, for the rectangular and circular cross-sections, respectively. To maintain the high accuracy while reducing the computation time, a sensitivity analysis was performed, and the maximum layer height was chosen as not to exceed 3 mm. The centroid of each concrete and steel layer is determined considering the appropriate geometrical expressions for both circular and rectangular sections. For concrete, temperature is obtained from the average distribution that would result in average compressive strength in each layer, whereas the maximum temperature reached is used directly for steel layers corresponding to the exact location of steel bars. The failure criterion of the RC element is defined by the crushing of concrete once the strain in any of the sectional layers reaches the residual ultimate strain (*εcuR*) proposed and validated by Alhadid and Youssef [24]. The restraining effect due to elevated temperature is considered in the analysis through calculating the axial restraint at each time increment depending on the assumed supporting condition. The axial force generated due to restraint is added to the initial applied load to determine the total axial load during fire exposure.

#### **7. Equivalent Residual Strain**

Residual stresses are induced in fire-damaged members for two main reasons:


Figure 9 illustrates the development of the strain components along section (A-A) of Figure 4c for rectangular sections. The same analysis procedure is considered for circular sections while accounting for the modified location of the steel layers. The difference between the residual thermal strain (*εthR*) and the residual transient strain (*εtrR*) is the total residual strain (*εR*), which can be either positive or negative depending on the temperature– load history and the magnitude of the developed transient strain. Due to the plane section

assumption, the deformed section is represented by a uniform equivalent strain (*εeq*) along the cross-section. Residual stress-induced strain (*εσ<sup>i</sup>* ) distribution is determined as the difference between an equivalent strain (*εeq*) and the total residual strain (*εR*). An iteration process is performed to evaluate the uniformly distributed equivalent strain (*εeq*) that satisfies the equilibrium condition of *εσ<sup>i</sup>* distribution. The value of *εeq* is determined such that the total axial force in concrete and steel resulting from *εσ<sup>i</sup>* distribution is equal to zero.

**Figure 9.** Development of various strain components along the discretized cross-section.

*εσ ε ε λ ε ε ε ε* Once equilibrium is achieved, *εσ<sup>i</sup>* is applied as initial strains in the concrete and steel layers, whereas *εeq* results in shifting the *P*-*ε* curve, as illustrated in Figure 10 for both rectangular and circular sections. The residual and equivalent strain distribution along column R3 and C3 cross-sections are shown in Figure 11. If the column is not initially loaded during fire exposure (*λ* = 0), then the residual equivalent strain (*εeq1*) is always negative, causing the *P*-*ε* curve to shift to the expansion side. However, by imposing an initial load to the column during the heating phase, a transient strain component develops and counteracts the influence of the thermal strain. If the applied load is large enough, the column experiences residual contraction instead of expansion after the cooling, as indicated by the positive equivalent strain (*εeq2*). The change in stiffness is attributed to the elimination of the residual stress-induced strains. Restraining the column affects the magnitude of the generated transient strain, especially if the column is not subjected to initial load. When the column is restrained, part of the equivalent strain (*εeq*) induces stresses within the section depending on the considered degree of restraint while maintaining the equilibrium condition. By restraining the column, additional compressive forces are developed in the column as a result of preventing the column's tendency to expand. *εσ ε ε λ ε ε ε ε*

(**a**) Rectangular columns (**b**) Circular columns

*ε*

*ε* **Figure 10.** Influence of initial load level on the residual (*P*-*ε*) relationship.

#### **8. Validation of the Proposed Analytical Model**

The capability of the present model to predict the post-fire structural performance of axially loaded RC members is validated in view of the experimental results by Chen et al. [25], Jau and Huang [26], Yaqub and Bailey [27] and Elsanadedy et al. [28]. The validation is limited to structural members made of normal-strength concrete where spalling does not occur.

Φ Φ Chen et al. [25] carried out a full-scale experiment to investigate the performance of RC columns after exposure to different fire conditions. The results obtained from the proposed analytical model are compared with the measured data of columns FC06 and FC05. These columns are exposed to an ISO 834 (2014) standard fire curve from four sides for 2 hrs and 4 hrs, respectively. The tested columns have cross-sectional dimensions of 300 mm × 450 mm, concrete cover of 40 mm and an overall length of 3.0 m. The concrete compressive strength at ambient conditions is 29.5 MPa. The longitudinal reinforcement consists of 4 Φ 19 mm and 4 Φ 16 mm steel bars with yield strengths of 476 MPa and 479 MPa, respectively. Both columns were subjected to an initial axial load of 797 kN prior to heat exposure. The specimens were axially loaded during the whole heating and cooling cycle. After 30 days from the fire test, the columns were subjected to a constant initial concentric load of 797 kN and an additional eccentric load offset a distance of 650 mm from the cross-sectional centre along the y-axis (weak axis) producing the bending moment about the x-axis, while another eccentric load is applied at 600 mm from the centroidal axis. Figure 12a shows the analytical and experimental load–deflection curves at the column mid-span due to the eccentric load about the y-axis. A very good agreement between both curves can be shown with a percent difference of 3.8% and 4.6% in the ultimate capacity of columns FC06 and FC05, respectively, and a percent difference of 6.3% and 5.4% in the 40%

secant stiffness for the same two columns, respectively. This variation can be attributed to the sensitivity of the adopted thermal expansion model to the experimental conditions and concrete mix.

(**c**) Using experiment by Yaqub and Bailey (2011) (**d**) Using experiment by Elsanadedy et al., (2016)

(**a**) Using experiment by Chen et al. (2009) (**b**) Using experiment by Jau and Huang (2008)

**Figure 12.** Validation of the proposed analytical model.

In another experimental study, Jau and Huang [26] investigated the residual behavior of initially loaded restrained RC columns subjected to heat from two adjacent sides. The cross-sectional dimensions of all columns are 300 mm × 450 mm, with an overall length of 2.7 m. The concrete cover varies between 50 mm or 70 mm, whereas the steel reinforcement ratio varies between 1.8% and 3.0%. Normal-strength concrete with a compressive strength of 33.7 MPa and steel bars with a yield strength of 475.8 MPa are used. The test setup allows the heat to flow through two adjacent surfaces only while the other two surfaces are insulated and not subjected to fire. The restrained columns are subjected to a 10% axial preloading of their ambient compressive strength during the 2 or 4 hr fire tests. After the columns naturally cooled down, the load is applied until failure occurs. Figure 12b shows both the experimental and predicted residual capacity of columns A12, B12, A14, A24 and B24 whose detailed geometrical and mechanical properties are provided by Jau and Huang [26]. The proposed model is found to predict the capacity of the tested columns with high accuracy, as indicated by the maximum percent error of 5.3% depicted for column A14 shown in Figure 12b. Overall, the agreement between the experimental and analytical results is very good. It is worth mentioning that exposing the specimens to fire from two adjacent sides only resulted in a lateral displacement in the range of 7 to 25 mm, depending on fire duration. Due to the influence of load–temperature interaction, the residual strength

and stiffness varies within the cross-section. The lateral displacement and the associated curvature should be considered when analyzing the fire-exposed columns, especially those with high slenderness ratios.

The influence of elevated temperature on the residual axial capacity, axial stiffness and stress–strain behavior of circular columns strengthened with fiber-reinforced polymers (FRP) was experimentally investigated by Yaqub and Bailey [27]. The unwrapped control specimen (i.e., Specimen No. 2) is considered for comparison. The examined column has a diameter of 200 mm and an overall length of 1000 mm. The concrete cover to the centroid of the steel bars was taken as 30 mm. The reinforcement consisted of 6 Φ 10 mm steel bars, resulting in a reinforcement ratio of 1.5%. Normal-weight concrete with a compressive strength of 42.4 MPa and steel bars with a yield strength of 570 MPa were used. The column was exposed to a predefined heating–cooling cycle 9 months after casting until the entire cross-section reached a uniform temperature of 500 ◦C. After that, the column was subjected to a displacement-controlled uniaxial compression load until failure. The member temperature at the time of the compression test was 22 ◦C. Figure 12c presents both the experimental and analytical axial load–deformation curves for the specimen, which was exposed to a uniform temperature of 500 ◦C before cooling. The proposed model is found to provide very good prediction of the experimental results, as indicated by the 4.2% percent error. The strength of the heat-exposed columns was reduced by 41.8% after the heating–cooling cycle, as implied by the strength reduction from an average of 1418 kN for the intact columns to 826 kN of the heated column. Based on Figure 4.4.2.2.1c(b) of ACI 216-14 [9], the estimated residual strength of the specimen at 500 ◦C is determined as about 51.0% of the initial compressive strength. This represents an error of about 12.4% with respect to the actual residual strength of 58.2% determined in the lab. The incremental stiffness at service load is almost identical between the two curves. Additionally, the load–deformation behavior obtained from the proposed model is shown to be consistent with that obtained experimentally in terms of stiffness, peak strain and failure strain.

Elsanadedy et al. [28] examined the effect of high temperature on the residual capacity and deformation behavior of R.C. columns strengthened with FRP wraps. The control specimens, which were unwrapped, were tested at a room temperature of 26 ◦C and are considered for comparison in this paper. All the examined columns have a diameter of 242 mm and an overall length of 900 mm. The concrete cover to the centroid of the steel bars was taken as 41 mm. The reinforcement consisted of 4 Φ 10 steel bars, resulting in a reinforcement ratio of 0.68%. Normal-weight concrete with a compressive strength of 42 MPa and steel bars with a yield strength of 593 MPa were used. The columns were exposed to elevated temperature along their circumference under unstressed conditions with a heating rate ranging between 5 ◦C and 15 ◦C per minute. Specimens C-200, C-400 and C-500 are considered for comparison, where the letter "C" indicates un-strengthened specimens, and the number indicates the maximum temperature reached in the oven. The specimens were subjected to the specified maximum temperature for 3 h before shutting down the oven. The columns were then naturally cooled inside the oven to room temperature. After that, the columns were taken out of the oven and subjected to a displacement-controlled uniaxial compression load until failure. Figure 12d presents both the experimental and analytical axial load–deformation curves for the examined specimens. The residual strength of specimens C-200, C-400 and C-500 were found to be 1745 kN, 1490 kN and 1350 kN, respectively. These values represent a residual strength of 90.1%, 77.1% and 69.9% of the initial strength of the intact specimen, respectively. The capability of the proposed model to capture the residual capacity of the heat-exposed columns is very good, as indicated by the 4.7%, 3.7% and 6.5% percent errors for specimens C-200, C-400 and C-500, respectively. Considering Figure 4.4.2.2.1c(b) of ACI 216-14 [9], the residual strength of specimens C-200, C-300 and C-400 are 84.0%, 75.0% and 63.0% of the initial compressive strength, respectively. This represents a percent error of 7.0%, 2.8% and 9.8% relative to the tested specimens, respectively. Additionally, the load–deformation behavior obtained from the proposed model is shown to be consistent with that obtained experimentally in terms of stiffness,

peak strain and failure strain. The error between the model and experimental results can be attributed to the variation in heating rate and the presence of residual surface cracks and initial misalignment, which are not accounted for in the model.

#### **9. Parametric Study**

The main parameters include the concrete compressive strength, *f<sup>c</sup> '* (25 MPa and 35 MPa); steel yield strength, *f<sup>y</sup>* (300 MPa and 400 MPa); fire duration, *t* (0.5 hr, 1.5 hrs and 2.5 hrs); initial load level, *λ* (0.0, 0.2 *f<sup>c</sup> '* , 0.4 *f<sup>c</sup> '* ); axial restraint stiffness ratio, *R<sup>D</sup>* (0.0, 0.5 and 1.0); and steel reinforcement ratio, *ρ* (0.02 and 0.04). The cross-sectional dimensions of the rectangular sections are defined in terms of member height, *h* (400 mm and 800 mm) and width, *b* (300 mm and 600 mm), whereas for circular sections, the geometrical properties are determined in terms of their diameter, *D* (350 mm and 650 mm). A 30 mm clear concrete cover was considered for all specimens. The members are exposed to fire along their perimeters according to ASTM E119 [17] standard fire curve, followed by a cooling phase according to ISO 834 [18] recommendations. The influence of the considered factors on the post-fire behavior of both rectangular and circular RC axially loaded members is investigated in view of a parametric study. Based on these parameters, the analytical investigation consists of a total of 1728 different cases.

The effect of the aforementioned parameters on both the residual axial capacity and the residual 40% secant axial stiffness is illustrated in view of the members presented in Table 1. The variation in the residual capacity and stiffness in terms of the different parameters at different initial load levels is presented Figures 13 and 14 for both rectangular and circular sections, respectively.

#### *9.1. Effect of Fire Duration*

Fire duration has been found to have the most significant influence on reducing the post-fire capacity and stiffness of both rectangular and circular RC columns. The influence of increasing the fire duration on the residual flexural behavior is examined in view of the rectangular sections (R1, R2 and R3) and the circular sections (C1, C2 and C3), as shown in Figures 13a and 14a, respectively. Prolonged exposure to fire results in material strength degradation and softening, which adversely affect the stiffness and capacity of the fire-damaged section. The permanent strength and stiffness reductions in the circular columns are found to be slightly higher than those with rectangular sections. This can be attributed to the higher maximum temperature reached within the circular sections subjected to fire for the same fire duration, as was previously described in Figure 6. The additional deterioration in both concrete and steel residual mechanical properties caused by the longer duration of the heating–cooling cycle provides more time for heat to transfer to the inner elementary layers raising their temperatures.

#### *9.2. Effect of Section Size*

Increasing the cross-sectional dimensions of both rectangular and circular columns results in higher residual flexural strength and stiffness after fire, as indicated in Figures 13b and 14b. This larger residual capacity is caused by the lower temperature increase within the larger member as it requires more heat energy to increase its temperature. This is attributed to the additional concrete cover provided by the larger sections causing the hindrance of heat transfer from the column perimeter towards its core. Hence, internal concrete fibers experience lower temperatures and consequently higher residual compressive strength and stiffness than the inner elements of columns with smaller dimensions. For the same fire duration, concrete within the inner parts of the wider member experience a lower increase in temperature and consequently more recovery after a fire. The influence of strength recovery in steel bars is neglected since concrete cover is the same in all specimens causing the maximum temperature reached in all steel bars to be the same.

**Figure 14.** Influence of varying the examined parameters on the axial capacity and stiffness of circular columns.

#### *9.3. Effect of Mechanical Properties*

Increasing the concrete compressive strength is found to have an insignificant inverse relationship on the reduction ratio of both capacity and stiffness for all load levels in the examined range, as shown in Figures 13c and 14c, for rectangular and circular columns, respectively. The decreasing rate can be justified by the greater reduction in compressive strength of the stronger concrete after fire. Hence, the reduction in concrete contribution within the compression zone becomes more pronounced and results in the observed larger decrease relative to the original capacity. The use of normal-strength concrete infers that no spalling is encountered, which could otherwise significantly affect the residual capacity. The same observation can be drawn by varying the grade of the embedded steel bars from 300 MPa to 400 MPa, as shown Figures 13d and 14d, for rectangular and circular columns, respectively. This is attributed to the fact the steel bars restore a significant portion of their capacity and stiffness after fire as discussed previously.

#### *9.4. Effect of Steel Reinforcement Ratio*

Steel bars are located near the exposed surfaces of the columns and are subjected to relatively high temperatures. However, this has negligible impact on the overall axial capacity and stiffness reduction due to the significant recovery of mild steel bars after fire exposure [29–31]. Figures 13e and 14e show that increasing the reinforcement ratio results in an insignificant increase in both residual capacity and stiffness in the rectangular and circular columns, respectively. This is attributed to the higher impact of the larger steel area in replacing the fire-damaged concrete since the recovery of steel bars is very significant as opposed to concrete.

#### *9.5. Effect of Restraint Conditions*

The influence of restraining the member against thermal expansion during heating has been found to slightly decrease its post-fire stiffness and capacity, as shown in Figures 13f and 14f, for both rectangular and circular columns, respectively. The reduction in residual properties is more pronounced when comparing the fully unrestrained sections with the restrained ones. However, the reduction seems to be almost identical for columns that are fully restrained or 50% restrained. This is explained by the impact of transient strain in changing the deformation behavior of axially loaded members during fire exposure through alleviating the thermal expansion. As the stiffness of the supports provided by the adjacent frame members increases, more restraining forces are generated to counteract the tendency of the column to expand. This additional force results in transient creep strain, which reduces the thermal strain and consequently decreases the amount of restraining force required to overcome the expansion. These two processes occur simultaneously and have a negative influence on each other, causing them to reduce the impact of restrains.

During fire exposure, the column's tendency to undergo thermal expansion increases with time, causing the support to counteract this potential movement, depending on the column's stiffness. Initially, the member's stiffness remains close to that at ambient conditions as the temperature increase within the member is relatively low. Thus, an increase in restraining force results in significant hindrance of the column's deformation as the thermal strain component increases. However, after a certain period of time, the temperature within the member becomes relatively high, causing the stiffness degradation to become more pronounced. Thus, the forces required to resist the larger thermal expansion of the member drops. The axial force required to restrain the member keeps decreasing as a result of the continuous reduction in stiffness caused by elevated temperatures. Therefore, the change in the restraining load is characterized by a mild increase followed by a gradual decrease with time.

#### **10. Proposed Simplified Expressions to Obtain Residual Axial Capacity and Stiffness**

Prolonged exposure of RC columns to elevated temperatures according to a standard fire has a substantial influence on their axial capacity and deformation behavior.

The residual structural performance of such columns relies on the geometrical characteristics, mechanical properties, initial load, restraint conditions and fire duration that should be appropriately accounted for in the analysis. Accurate determination of temperature distribution and residual strain components developed within RC columns is tedious and requires detailed thermal and structural analyses that may not be convenient for design engineers. The proposed analytical model comprehensively addresses the influence of the aforementioned factors on determining the post-fire response of both rectangular and circular RC columns. Hence, based on the extensive parametric study conducted on the 1728 different cases, regression analysis is carried out to develop expressions for obtaining both the residual axial capacity and secant axial stiffness of fire-damaged rectangular and circular RC columns. These proposed expressions take into consideration the loading history, restraint conditions, fire duration, material strength and cross-sectional dimensions of the exposed members. The validity and accuracy of the proposed equations depend on the range of parameters considered in the parametric study. The proposed expressions provide a suitable approach for predicting the behavior of RC columns after exposure to an extreme standard fire scenario. This would be a valuable tool for both researchers and engineers to predict the post-fire performance of RC columns during the design phase.

#### *10.1. Rectangular Sections*

Linear multiple regression analysis is performed to propose an expression for both the residual capacity and axial stiffness ratios (*ω*), as given in Equation (4).

$$
\omega = A\_1 + A\_2 \lambda + A\_3 f\_\varepsilon' + A\_4 f\_y + A\_5 \rho + A\_6 \frac{\rho f\_y}{f\_\varepsilon'} + A\_7 b + A\_8 h \tag{4}
$$

where *λ* is the initial load level relative to ambient capacity, *f* ′ *c* is the concrete compressive strength (MPa), *f<sup>y</sup>* is the steel yield strength (MPa), *ρ* is the steel reinforcement ratio, *b* is section width (m), and *h* is section height (m). The coefficients (*A<sup>i</sup>* = 1, 2, 3, 4, 5, 6, 7, 8) are given in Table 2 in terms of the axial restraint ratio (*RD*) and fire duration at the end of the heating phase (*t*) in hours. For values other than the listed *t* and *RD*, linear interpolation of the upper and lower calculated *ω* should be performed. In Table 2, *P<sup>o</sup>* and *P<sup>r</sup>* are the axial capacities at ambient and post-fire conditions, respectively; *EA<sup>i</sup>* and (*EA<sup>i</sup>* )*<sup>r</sup>* are the initial axial stiffness at ambient and post-fire conditions, respectively; *EA*0.4 and (*EA*0.4)*<sup>r</sup>* are the 40% axial stiffness at ambient and post-fire conditions, respectively; and *EA*0.8 and (*EA*0.8)*<sup>r</sup>* are the 80% axial stiffness at ambient and post-fire conditions, respectively.

It is worth mentioning that although the rectangular column is exposed to fire from all sides, the coefficients of the section height (*h*) and section width (*b*) are different in Equation (4). This variation is attributed to the assumed reinforcement configuration where the steel bars lie in two opposite layers that are parallel to the section width as indicated in Figure 4a.

The applicability of the proposed expressions is assessed by comparing the values obtained using the proposed equations and the results obtained from the analytical analysis. A comparison between the values predicted from Equation (4) and the results determined through performing detailed analytical analysis for all examined cases revealed a very good agreement, as shown in Figures 15a and 16a, for both residual capacity and axial stiffness, respectively. The equality line denotes the location on the graph where the predictions from the proposed equations match those obtained from the proposed analytical model. As shown in the figure, the data points are uniformly distributed in the vicinity of the equality line.

The residual compressive strength of column R6 is determined from ACI 216.1-14 and compared to that obtained from Equation (4) considering an exposure of 1 h to ASTM E119 [17] standard fire. Figure 4.4.2.3a and 4.4.2.2.1c(b) of ACI 216.1-14 provide the temperature distribution and the residual compressive strength of concrete at various heating and loading conditions, respectively. The unstressed residual compressive strength obtained from the ACI procedure for column R6 is found to be just under 71.0% of its initial strength.  

ሺ ሻ

Considering the same parameters, the percentage of the residual strength obtained from the proposed Equation (4) is found to be 77.7%. In general, there is a good agreement between the two values considering the complex behavior of fire-exposed RC members. The variation between the two values is attributed mainly to the difference between the exposure and boundary conditions assumed in both methods. The residual strength is calculated from Equation (4) considering the reinforcement ratio, steel yield strength and section height, which is not specifically provided in the ACI procedure. − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> <sup>−</sup> − <sup>−</sup> − <sup>−</sup> <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup>

− − − − − − − − −

− <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup>

− <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup> − <sup>−</sup>


**Table 2.** Coefficient of Equation (4) for rectangular sections. − <sup>−</sup> <sup>−</sup> <sup>−</sup> − <sup>−</sup> <sup>−</sup> <sup>−</sup> − <sup>−</sup> <sup>−</sup> <sup>−</sup>

#### *10.2. Circular Sections*

Multiple linear regression analysis is also performed to propose a similar expression for the residual capacity and stiffness of the axially loaded circular RC columns, as shown in Equation (5).

$$
\omega = B\_1 + B\_2 \lambda + B\_3 f\_c' + B\_4 f\_y + B\_5 \rho + B\_6 \frac{\rho f\_y}{f\_c'} + B\_7 D \tag{5}
$$

where *D* is the diameter of the cross-section (m). The coefficients (*B<sup>i</sup> =* 1, 2, 3, 4, 5, 6, 7) are given in Table 3 in a similar manner to the coefficients of the rectangular section. The line of equality plot reveals that the proposed expressions provide an excellent prediction of the capacity and stiffness compared to the results obtained from the analytical model, as illustrated in Figures 15b and 16b, respectively. The presence of outliers is almost negligible, which enhances the confidence of using the proposed expressions. The simplicity and robustness of the proposed expressions is an advantage for increasing their applicability during the design phase.

(**a**) Rectangular section (**b**) Circular section

**Figure 16.** Validation of the proposed Equations (4) and (5) for residual axial stiffness.


**Table 3.** Coefficient of Equation (5) for circular sections.

#### **11. Application of the Proposed Procedure**

The proposed method is suitable to be implemented by engineers during the preliminary design phase for estimating the residual performance of RC frames exposed to

extreme standard fire conditions. The current study represents a step toward developing an integrated approach for considering all the components of the RC frames subjected to different loading conditions and exposed to various fire curves. This research assumes that the global behavior of the frame system is merely affected by the deterioration taking place in columns subjected to pure axial loads. This implies that beams and eccentrically loaded columns are either perfectly insulated against fire or are not exposed to critical temperatures capable of affecting their residual performance. The proposed procedure considers the interaction between the entire frame system and the fire-damaged columns in terms of connections' stiffness and load path. The fire-exposed columns are considered in the analysis as isolated members using an equivalent spring model whose stiffness is determined from the stiffness of the entire frame.

The steps required to adopt the proposed procedure are discussed in view of the 20-storey frame structure shown in Figure 17. The frame is composed of 8 m-long 300 × 450 mm RC beams made of normal-weight concrete with *f<sup>c</sup> '* of 35 MPa and reinforced with grade 400 MPa steel bars. The 300 × 400 mm columns are 3.6 m long with the reinforcement ratio of 0.04 and are constructed of the same materials as the beams. The moment of inertia of both member types is determined assuming cracked cross-sections (i.e., *Ibeam* = 0.35*I<sup>g</sup>* and *Icolumn* = 0.7*Ig*), where *I<sup>g</sup>* is the gross moment of inertia of the considered member. The frame is loaded by subjecting the beams to a uniformly distributed load of 33 kN/m along the entire span. ASTM E119 standard fire is assumed to spread in the first floor of the building for 1.5 h, followed by a gradual cooling phase, according to ISO 834 specifications. Beams and corner columns are assumed to not be significantly influenced by fire, while the interior columns (i.e., columns IC1 and IC2) are exposed to fire from all sides. To determine the residual performance of the frame, the proposed procedure is discussed with reference to column IC1 in Figure 17. The structural analysis is performed using the commercially available ETABS [32] finite element software.


(**b**) Unit load at the top joint


(**a**) Part of the considered loaded frame (**c**) Unit load at bottom joint

*δ*

**Figure 17.** Description of the proposed analysis procedure.

*δ δ* (1) Determine the equivalent axial stiffness (*k<sup>δ</sup>* ) of the spring shown in Figure 3b that represents the vertical stiffness of the structural system at that point. This is performed by replacing the examined column with a unit load acting at each joint individually, as shown in Figure 17b,c. The structural analysis is then performed on the frame to find the corresponding displacement of the considered joint. *k<sup>δ</sup>* for each joint is calculated as the ratio between the unit load to the induced displacement. The total equivalent

> ሺ<sup>ఋ</sup> ሻଵ ሺ<sup>ఋ</sup> ሻଶ

> > ሻ<sup>ଵ</sup> + ሺ<sup>ఋ</sup>

ሻଶ

*δ*

ሺ<sup>ఋ</sup>

*δ δ*

*λ*

*λ*

*δ*

<sup>ఋ</sup> =

axial stiffness (*k<sup>δ</sup>* ) is then determined by considering the two joints as springs in series according to Equation (6).

$$k\_{\delta} = \frac{(k\_{\delta})\_1 (k\_{\delta})\_2}{(k\_{\delta})\_1 + (k\_{\delta})\_2} \tag{6}$$

In this example, (*k<sup>δ</sup>* )<sup>1</sup> is determined as 10,000 kN/m, while (*k<sup>δ</sup>* )<sup>2</sup> is found to be 829,187 kN/m. Thus, *k<sup>δ</sup>* for the isolated column model is 9881 kN/m.


#### **12. Conclusions**

In this paper, both thermal and sectional analyses are performed to determine the residual capacity and stiffness of fire-damaged rectangular and circular columns in typical RC frames. The temperature–load history experienced by the exposed members is considered in detail in the analytical study. The model is validated against relevant experimental studies found in the literature. A parametric study is carried out to determine the influence of various loading conditions and fire scenarios on the residual properties of the members. An objective-based method is then proposed to assist the engineers in evaluating the residual behavior of axially loaded RC columns considering an extreme standard fire scenario. The applicability of the proposed procedure is limited to RC columns made of normal-weight concrete and siliceous aggregate with fire durations up to 2.5 h, initial load level up to 0.4 *f<sup>c</sup> '* , section height between 400 mm and 800 mm, section width between 300 mm and 600 mm, section diameter between 350 mm and 650 mm, and steel reinforcement ratio between 2% and 4%. The main findings are as follows:


**Author Contributions:** Conceptualization, M.A.Y.; data curation, M.M.A.A.; investigation, M.M.A.A.; writing—original draft preparation, M.M.A.A.; writing—review and editing, M.A.Y.; acquisition, M.A.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC), and Western University.

**Conflicts of Interest:** The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.

#### **Nomenclature**


#### **References**


**Alaa T. Alisawi \* , Philip E. F. Collins and Katherine A. Cashell**

Department of Civil and Environmental Engineering, Brunel University London, London UB8 3PN, UK; Philip.Collins@brunel.ac.uk (P.E.F.C.); Katherine.Cashell@brunel.ac.uk (K.A.C.) **\*** Correspondence: Alaa.Al-isawi@brunel.ac.uk

**Abstract:** The probability of extreme events such as an earthquake, fire or blast occurring during the lifetime of a structure is relatively low but these events can cause serious damage to the structure as well as to human life. Due to the significant consequences for occupant and structural safety, an accurate analysis of the response of structures exposed to these events is required for their design. Some extreme events may occur as a consequence of another hazard, for example, a fire may occur due to the failure of the electrical system of a structure following an earthquake. In such circumstances, the structure is subjected to a multi-hazard loading scenario. A post-earthquake fire (PEF) is one of the major multi-hazard events that is reasonably likely to occur but has been the subject of relatively little research in the available literature. In most international design codes, structures exposed to multi-hazards scenarios such as earthquakes, which are then followed by fires are only analysed and designed for as separate events, even though structures subjected to an earthquake may experience partial damage resulting in a more severe response to a subsequent fire. Most available analysis procedures and design codes do not address the association of the two hazards. Thus, the design of structures based on existing standards may contribute to a significant risk of structural failure. Indeed, a suitable method of analysis is required to investigate the behaviour of structures when exposed to sequential hazards. In this paper, a multi-hazard analysis approach is developed, which considers the damage caused to structures during and after an earthquake through a subsequent thermal analysis. A methodology is developed and employed to study the nonlinear behaviour of a steel framed structure under post-earthquake fire conditions. A three-dimensional nonlinear finite element model of an unprotected steel frame is developed and outlined.

**Keywords:** fire; earthquake; finite element analysis; Abaqus; multi hazard analysis

#### **1. Introduction**

Extreme events such as earthquakes, fires or blasts have a low likelihood of incidence during a structure's lifecycle but they can have tremendous after-effects with regard to the safety of any inhabitants and the integrity of the structure. In addition, there may be a higher risk of a second extreme event occurring, owing to any damage that occurs during the initial event, for example, a fire after an earthquake [1,2]. In such a case, the structure is exposed to multiple hazards. The current paper is concerned with the response of steel framed structures when subjected to an earthquake that is followed by a fire. This particular multi-hazard event is known as a post-earthquake fire (PEF). Most structures are required to satisfy 'life safety' design criteria as specified in design standards. These codes guarantee that structures remain stable and continue to carry gravity loads, dead loads and a percentage of live loads during extreme events, thus allowing the building's occupants to evacuate the buildings safely [3,4]. Based on the function of the structure and its importance, the allowable rate and type of damage that is tolerable during an extreme loading is typically specified during its design. The design codes ensure building safety under a variety of load combinations that represent different extreme loading scenarios.

**Citation:** Alisawi, A.T.; Collins, P.E.F.; Cashell, K.A. Nonlinear Analysis of a Steel Frame Structure Exposed to Post-Earthquake Fire. *Fire* **2021**, *4*, 73. https://doi.org/10.3390/ fire4040073

Academic Editor: Maged A. Youssef

Received: 2 September 2021 Accepted: 6 October 2021 Published: 15 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

However, the load combination of an earthquake followed by a fire has yet to be included in international design standards although the forces and moments applied to a structure during a PEF are likely to be much greater than for individual extreme events [4,5].

Mitigating the effects of PEF on buildings during the design process in order to ensure the safety of occupants and emergency service personnel is a crucial aspect to consider for any PEF safety strategy. The effects of a PEF can be diminished by controlling and determining the status of structural stresses after the first event (the earthquake) and also designing and/or strengthening the building to withstand and survive the fire loading. Eurocode 8 Part 1 [6] provides a design load combination for a set of different actions (Equation (1)). These actions must be combined with those from other loads, such as permanent loads (G), pre-stressing loads (P), seismic actions (AE,d) and a proportion of the variable (live) loads (Q). A specific reduction factor (Ψ2,i ) is provided in Eurocode 8 and the recommended values of factors for buildings are specified in Eurocode 3 Part 1–2 [7]. ሺA,ୢ ሺΨଶ,୧

$$\sum\_{\mathbf{i}\geq 1} \mathbf{G}\_{\mathbf{k},\mathbf{j}} + \mathbf{P} + \mathbf{A}\_{\mathbf{E},\mathbf{d}} + \sum\_{\mathbf{i}\geq 1} \mathbf{\varPsi}\_{2,\mathbf{i}} \ \mathbf{Q}\_{\mathbf{k},\mathbf{i}} \,\tag{1}$$

There are two important concepts that should be considered when designing a structure that can resist different magnitudes of earthquakes, which are frequent earthquakes and design earthquakes. The return period of a frequent earthquake is lower than that of a design or 'maximum considered' earthquake. A design earthquake is characterized by a return period R of 475 years, which corresponds to a 10% probability of exceedance in 50 years. As shown in Figure 1, a usual building must be operational for a frequent return period, and safe in the zone of a design earthquake. For very important structures, the critical components must remain operational for a 'maximum considered' earthquake [8,9].

**Figure 1.** Requirements for structural performance during different types of earthquake in accordance with EN 1998-1 [6].

In this context, it is clear that in order to develop appropriate design methods for a PEF event, it is critical to first develop a good understanding of the complex structural behaviour that occurs in this scenario. The structural behaviour and material properties of the remaining parts of the structure after the first hazard are classified as the input properties of the structure during the fire, and it is important that these are accurately represented. For this reason, in the current paper, a multi-hazard analysis approach is presented for steel-framed buildings. The paper proceeds with an overview of the state-

of-the-art, which is followed by a description of the three-dimensional (3D) finite element (FE) model that was developed using the Abaqus software [10]. The damage caused to a structure during and after an earthquake is included in the sequential thermal analysis. This methodology is developed and employed to study the nonlinear behaviour of a steel-framed structure when subjected to the PEF loading condition.

#### **2. State of the Art**

There has been limited research into multi-hazard extreme events and their effects on building structures compared with single extreme events such as a fire or an earthquake. Nevertheless, as more has become known and understood about single hazard events, researchers have begun to study the more complex case of PEF [1–3,11]. Della Corte et al. [12] investigated the fire resistance rating for unprotected steel frames for the PEF condition, assuming elastic-perfectly plastic steel behaviour. This study considered second-order effects, whereby the lateral displacements caused by the stresses and strains resulting from the earthquake, reduce the structural stability under gravity loads. However, this study did not include stiffness degradation in the analysis.

Ali et al. [13] conducted a comprehensive study that considered the effects of geometry and stiffness degradation in the PEF condition, in which they also developed of a 3D numerical model. The behaviour of an unprotected, single-storey, multi-bay steel frame was analysed after its exposure to a seismic load followed by a sizeable uncontrolled fire. It was shown that the PEF resistance is significantly dependent on both the particular fire scenario as well as the gravity loads that are applied to the structure. Mousavi et al. [14] presented a review on the key issues and hazards related to PEF for a building and found that the principle influential factors are the intensity and duration of the earthquake and fire, the level of protection included in the original design and the structural materials used. Zaharia and Pintea [15] examined two types of steel frames which were designed for different return periods of ground motion (2475 and 475 years, respectively). The seismic response of the system was evaluated by conducting a nonlinear static analysis, i.e., a pushover analysis. The structure that was designed for a return period of 475 years suffered from a more significant inter-storey drift in the plastic range after the earthquake event, whilst the frame designed for the longer return period continued to respond in the elastic range. A fire analysis was then performed for both frames and the results showed that the fire resistance of the frame with a shorter return period, which had experienced greater deformations during the earthquake, was less than for the other frame, which did not have a history of plastic deformations before the fire.

Ghoreishi et al. [16] presented a review of the existing experimental and numerical studies on structural systems when subjected to fire, which included a multi hazard analysis of PEF. This study revealed that traditional design methods based on the concept of fire resistance ratings do not consider many of the significant typical structural conditions such as size, control conditions and loading. Moreover, the fire resistance of a singular structural element is different to that of the overall structure, due to the influences of continuity, interaction between elements and load and stress redistribution. Memari et al. [17] presented their insights into the consequences of PEF on low-, medium- and high-rise steel moment-resisting frames, using FE and nonlinear time-history analysis. An uncoupled thermal-mechanical analysis was conducted and a fire was applied at the reduced beam section connections (RBS). The material properties were assumed to be elastic-perfectly plastic in this analysis, but it is noteworthy that one-dimensional beam elements were employed to represent the structure's components that were incapable of depicting local buckling failure in the members.

Chicchi and Varma [1] published a state-of-the-art review for the analysis and the design of moment-resisting framed structures subjected to PEF, which was largely focused on events in the USA. This review included an assessment of the consequences of non-structural damage produced through earthquakes on the subsequent structural fire resistance. A methodology was proposed for analysing and designing these types of

structures, so that they may resist a PEF event using incremental dynamic and fire analyses. Zhou et al. [18] proposed an integrated multi-hazard analysis framework using FEA and the OpenSEES software. This framework provides a practical solution for measuring the residual fire resistance of a system with cementitious passive fire protection (PFP) subjected to fire following a moderate earthquake. However, it is noteworthy that this study analysed individual structural members rather than the overall structure.

The research that has been conducted to date generally illustrates that the behaviour of a building subjected to a PEF is not significantly affected by the nonlinear geometric effects caused by an earthquake if the initial design of the structure complies with the serviceability limit state requirements. However, there are shortcomings in some of the assumptions that have been made in the available research, including simplifications of the element types, methods of analysis and the applied input motions. The nonlinear geometric effects are generally assumed without considering the influence of structural resonance and the frequency effect. Moreover, if an inaccurate design spectrum is determined, in accordance with Eurocode 8, the acceleration time history applied during the seismic stage of the multi-hazard event could lead to an underestimation of the stresses and strains experienced in the structure. Such is the basis for this work, which provides a novel approach to quantifying the effect of a PEF event on structural behaviour, using a coupled nonlinear sequential analysis. The study highlights the unique relationship between the geotechnical and geological properties of the applied motion during the earthquake stage and the system behaviour during a multi-hazard event. The coupled nonlinear time-history analysis is used to identify the residual material properties of the subsequent fire analysis.

#### **3. Basis of the Analysis**

It is clear that an accurate evaluation of a structure's response following an earthquake, which serves as the input data in the fire analysis for a PEF event, is critically important. Its response is influenced by many factors including the level of certainty of the material properties and the mechanical behaviour of the structural components as well as the intensity of the seismic action (e.g., [19]). These difficulties and uncertainties have led researchers to adopt simplified approaches for assessing the seismic structural behaviour and damage in PEF analyses [20,21]. However, simplified methods may not present an accurate depiction of the actual structural behaviour following an earthquake, particularly for the stress redistributions that occur and are likely to be quite influential in its fire performance (e.g., [22,23]). The key problem lies in the appraisal of the physical condition of the structure following the earthquake, or the 'initial condition' for the subsequent fire action.

During most major earthquakes, structures are required to withstand significant levels of plastic deformation. The availability of reliable analytical methods, including sophisticated numerical models, may facilitate a more realistic reflection of the performance and damage of a structure when subjected to an earthquake. The structural damage experienced can be classified as either geometric, whereby the initial geometry is altered due to plastic deformations that occur during the earthquake, or mechanical, i.e., the degradation of the mechanical properties of the structural components that are in the plastic range of deformation during the earthquake.

#### *3.1. Seismic Analysis for PEF*

Traditionally, the effects of an earthquake on a structure are studied using either approximate methods, such as a pushover analysis, or a time-history analysis. A pushover analysis is a nonlinear static analysis procedure used to estimate the strength of a structure beyond its elastic limit but does not induce actual plastic damage in the structure and does not require a ground motion time history. On the other hand, a time-history analysis is a nonlinear dynamic response analysis performed using an actual or artificial earthquake to evaluate the response of the system. A time-history analysis usually takes significantly longer to complete compared to a pushover analysis and is also more computationally demanding. However, it provides a more accurate depiction of the structural response to a seismic event, which is imperative in a PEF assessment. When the damage from an earthquake is underestimated, a structure can be highly vulnerable to failure even if it has been rigorously designed for an isolated fire condition. It is in this context, that this study applies a time-history analysis to assess the structural response to the seismic excitation.

#### *3.2. Input Data*

The earthquake input data is generated in accordance with the structure frequency modes, geotechnical and geological site properties, and the design response spectrum characteristics. In a performance-based design, a structure subjected to a design earthquake should maintain the required design-level performance [24]. Eurocode 8 specifies two types of earthquakes, namely Type 1 and Type 2 spectra and also four different importance classifications for buildings, depending on their function. In the current work, it is assumed that the structure being analysed has an importance classification of III (i.e., buildings with a seismic resistance that is of importance due to the consequences associated with a collapse, e.g., schools, assembly halls, cultural institutions, etc.) and is therefore subjected to a Type 2 earthquake. The ground conditions are Type E as defined in Eurocode 8, described by various stratigraphic profiles and parameters and with viscous damping set at 5%. For these conditions, the peak ground acceleration (PGA) that occurs during the earthquake is 0.35 g.

The design response spectrum is also developed in accordance with Eurocode 8 for selected targeted time histories. The user-selected time histories are subjected to a scaling and matching procedure to derive earthquake input data within the spectrum periods of interest. The spectral scaling method used in the current study employs a computer algorithm—using SeismoSignal and SeismoMatch software [25]—to modify the real and artificial time histories in order to closely match the target design response spectrum. Using these procedures, data from a real earthquake are modified to a PGA of 0.35 g and a frequency content according to the design conditions.

To examine the seismic structural response, two predominant periods are selected for the modified real earthquake, namely 0.24 sec and 0.36 sec, in addition to one predominant period of 0.16 sec for the artificial motion. For the latter, a MATLAB algorithm has been developed to create the white noise artificial earthquake to satisfy the Eurocode 8 value of the structural natural period; there are more details on this later. The SeismoSignal and SeismoMatch software are combined with data from the U.S. Geological Survey (USGS) peer database [26] to meet the spectral design requirements. Figure 2a illustrates the Eurocode 8 design response spectrum with the modified real earthquake spectra with predominant periods of 0.24 sec and 0.36 sec, respectively, and the corresponding acceleration time histories are shown in Figure 2b. Figure 3 represents the corresponding data for a spectrum with a predominant period of 0.16 sec, for the artificial motion.

#### *3.3. Thermal Stress Analysis in PEF Analysis*

In the post-earthquake fire analysis, the deformed or damaged structural configuration that occurs following the earthquake event is employed as the input for the application of the thermal loads [27,28]. For the fire load, a uniform standard ISO-834 fire exposure [29] is applied to all the components of the frame, as shown in Figure 4. The frame is made from mild steel with a yield and ultimate strength, at the ambient temperature, of 385 N/mm<sup>2</sup> and 450 N/mm<sup>2</sup> , respectively. The steel has a density of 7850 kg/m<sup>3</sup> and a coefficient of thermal expansion (αs) of 1.4 <sup>×</sup> <sup>10</sup>−<sup>5</sup> . The changes in material properties resulting from increasing levels of elevated temperature are obtained from the reduction factors provided in Eurocode 3 Part 1–2 [7].

**1.4**

**Acceleration (g)**

**0.4**

Predominant period=0.24 sec

**Figure 2.** Comparison of the real and design earthquake input data including (**a**) the design response spectrum and (**b**) the acceleration time histories.

**Figure 3.** Comparison of the artificial and design earthquake input data including (**a**) the design response spectrum and (**b**) the acceleration time histories.

**Figure 4.** Standard fire curve [7].

#### **4. Development of the Numerical Model**

#### *4.1. General*

A geometrically and materially nonlinear three-dimensional model of an unprotected single-storey steel frame has been developed using the Abaqus software, in order to analyse the behaviour of the given structure during a post-earthquake fire (PEF). The frame is fabricated from beams and columns of the same I-shaped cross-section, which are connected with rigid joints. The frame is 5720 mm in length, 5370 mm in width and has a height of 4050 mm. The cross-section has a depth (D) of 350 mm, flange width (B) of 170 mm, identical web (t) and flange (T) thicknesses of 10 mm each, root radius (r) of 12 mm and a depth between the flange fillets (d) of 306 mm. The frame is designed to withstand gravity and seismic loads in accordance with Eurocode 8 Part 1 [6]. In accordance with the basis for design information provided in EN 1990 [30] and the guidance on actions in EN 1991 [31], the frame has been designed for a load combination comprising of 100% of the permanent actions and 60% of the variable actions during the PEF event, as discussed later.

#### *4.2. Elements, Meshing and Boundary Conditions*

The steel sections are modelled through the finite element model using general purpose linear brick elements with reduced integration, referred to as C3D8R in the Abaqus library [32]. A mesh sensitivity study was conducted to achieve the optimal combination of accuracy and computational efficiency, which resulted in element sizes ranging between 10 × 20 mm and 20 × 20 mm at the beam-column connections and 10 × 100 mm and 20 × 100 mm for the rest of the beam/column steel sections. The steel is represented using a nonlinear elastoplastic material model which has a yield and an ultimate strength of 385 N/mm<sup>2</sup> and 450 N/mm<sup>2</sup> , respectively. These properties degrade with an elevated temperature in accordance with the reduction factors provided in Eurocode 3 Part 1–2 [7]. The beam-column connection is achieved using the tie condition. The base of the columns are assumed to rest on a rigid foundation system, so the earthquake boundary condition is applied at the base of all the columns. A roller support is used to constrain the displacement, placed vertically at the bottom of the model. The horizontal boundary conditions permit 'free' horizontal shaking in the direction/directions of the applied seismic load.

#### *4.3. Loading and Solution Procedure*

The analysis is performed sequentially, comprising of static, dynamic and thermal analysis steps, as illustrated in Figure 5. The analysis is carried out in three main multihazard analysis steps, as well as an initial sub-step. Firstly, a linear perturbation–frequency step is conducted to identify the structural modal analysis (as discussed in more detail later) and frequency content window of the dynamic system. Then, in the first analysis stage, a nonlinear static analysis is conducted, and the gravity loads are applied. The permanent loads are assumed to have a value of 8 kN/m<sup>2</sup> whilst the variable actions are equal to 2.5 kN/m<sup>2</sup> , in accordance with EN 1991 [31], and all permanent and variable actions are applied. In the second step, the earthquake is simulated through a nonlinear implicit dynamic analysis. The acceleration time history is applied at the base of the structure while the static loads remain constant. The time history is processed, filtering for window frequencies matching the system modes and the natural frequency of the structure during an earthquake with a PGA of 0.35 g. In the third analysis stage, the thermal loads are applied to the deformed structure in the form of a time–temperature curve. The load combination in this stage is considered to be 100% of the permanent loads acting together with 60% of the variable actions [31]. The overall analysis is performed in a sequence to carry forward the deformations, stresses and damage caused to the structure during one stage to the next stage of the analysis. The key objective of the current study is to compare between the structural behaviour of structures subjected to a multi-hazard event with the behaviour of those exposed to a fire-only scenario. Thus, to compare with and examine the consequences of an earthquake directly preceding and possibly causing a fire, a fire-only event is also studied.

**Figure 5.** Methodology of the sequential analysis.

#### **5. Results and Analysis**

In this section, the results of the finite element analysis are presented and discussed. The first results presented are for the frequency analysis, in which a linear perturbationfrequency analysis is developed as a sub-step of analysis, followed by the results from the PEF structural simulations.

#### *5.1. Frequency Analysis*

The natural period of vibration of a dynamic system is an essential factor for the forcebase design methodology ([33–35]). In this method, the base shear is the expected ultimate lateral load applied at the base of the structure during seismic activity. The natural period of vibration is a critical parameter in defining the design response spectrum and consequently in controlling the value of the base shear force. Hysteretic damping is applied in the restoring force, and viscous damping is considered by Rayleigh (proportional) damping, as provided in Equation (2):

$$\left[\mathbb{C}\right] = \mathfrak{a}\_M \left[M\right] + \mathfrak{f}\_K \left[\mathbb{K}\right] \tag{2}$$

where *α<sup>M</sup>* and *β<sup>K</sup>* are the mass and stiffness proportional damping coefficients, and [M], [K], and [C] are the mass, stiffness, and damping *n* × *n* matrices, respectively. The damping ratio of the system for different natural frequencies (ξ<sup>i</sup> ) can be determined using Equation (3):

$$\mathfrak{J}\_{i} = \frac{1}{2} \left[ \frac{\mathfrak{a}\_{c}}{\omega\_{i}} + \mathfrak{f}\_{c}\omega\_{i} \right] \tag{3}$$

In this expression, *ω<sup>i</sup>* is the system-mode frequency. Owing to the orthogonality between the system mode and damping matrix, as well as the assumption of 5% damping for the system modes, the corresponding mass and stiffness coefficients of Rayleigh damping are calculated using Equations (4) and (5), respectively:

$$\alpha\_M = \frac{2\omega\_i\omega\_j}{\omega\_j^2 - \omega\_i^2} \left(\mathfrak{f}\_i\omega\_j - \mathfrak{f}\_j\omega\_i\right) \tag{4}$$

$$\beta\_K = \frac{2\left(\mathfrak{f}\_j \omega\_j - \mathfrak{f}\_i \omega\_i\right)}{\omega\_j^2 - \omega\_i^2} \tag{5}$$

where *ω<sup>i</sup>* and *ω<sup>j</sup>* are any two system-mode frequencies and *ξ<sup>i</sup>* and *ξ<sup>j</sup>* are the damping ratio at *ω<sup>i</sup>* and *ω<sup>j</sup>* , respectively. International design codes provide empirical formulae to estimate the fundamental period of vibration *T* of the structure. Eurocode 8 Part 1 [6] recommends using the Rayleigh method, as presented in Equation (6):

$$T = 2\pi \sqrt{\frac{\sum\_{i=1}^{n} \left(m\_{i} \cdot S\_{i}^{2}\right)}{\sum\_{i=1}^{n} (f\_{i} \cdot S\_{i})}} \tag{6}$$

in which *m<sup>i</sup>* represents storey mass, *f<sup>i</sup>* represents horizontal forces, and *S<sup>i</sup>* is the displacement of masses caused by horizontal forces. The first six natural vibration periods, the damping coefficients, and the natural vibration period of the system have been computed based on a linear perturbation-frequency analysis in accordance with EN 1998-1, and the findings are shown in Table 1. Figure 6 presents the corresponding mode shapes. In addition, Table 1 presents each of these natural vibration periods together with the value determined using EN 1998-1. The data presented in Table 1, together with the mode shapes in Figure 6, indicate that the first natural period, computed according to Eurocode 8 provisions, (0.16 sec) is between the second (0.296 sec) and third (0.106 sec) mode of the simulated values. It is also evident that the estimated natural period values decrease significantly for the first two modes after which the reduction changes more gradually for the remaining modes. Due to this, it has been concluded that it is important to consider more modes than just the first mode of the system in the seismic analysis, as has traditionally been the case. Accordingly, three input motions are considered in this paper, with natural vibration periods of 0.24 sec, 0.36 sec and the Eurocode 8 value of 0.16 sec, respectively.

**Table 1.** First six natural vibration periods and factors of Rayleigh damping.


**Figure 6.** First six mode shapes for the steel framed structure following the frequency analysis.

#### *5.2. Validation Study*

Owing to a dearth of physical test data on a complete 3D structure, the numerical model is validated through a previously verified modelling approach, using the OpenSees FE software [14]. OpenSees (Open System for Earthquake Engineering Simulation) was initially developed at the University of California, Berkeley for seismic loading analysis [36] and was later extended to perform structural fire analyses at the University of Edinburgh [37]. Usmani et al. [37] found that OpenSees is capable of providing an accurate depiction of structural performance during fires. In this study, an identical steel frame has been modelled using OpenSees, and the results are presented in Figure 7, including (a) the time-displacement response for the fire-only scenario, (b) the temperature-displacement response for the fire-only scenario, (c) the time-displacement response for the PEF scenario and (d) the temperature-displacement response for the PEF scenario. All of the presented results are obtained from the mid-span location and the results from both the Abaqus

and OpenSees models are presented. It is clear that both models and approaches provide almost identical results.

**Figure 7.** Comparison of Abaqus with OpenSees simulations, including (**a**) the time-displacement record for the fire-only scenario, (**b**) the temperature-displacement record for the fire-only scenario, (**c**) the time-displacement record for the PEF scenario, and (**d**) the temperature-displacement record for the PEF scenario.

#### *5.3. Post-Earthquake Fire*

In this section, the FE model developed in Abaqus that has been previously described is employed to assess and understand the post-earthquake fire (PEF) behaviour of steel framed structures. As stated before, the nonlinear sequential analysis [5] comprises a static stage, followed by the time history earthquake analysis after which the fire is applied. In the seismic analysis, the structure is subjected to two different time-history motions (referred to a Case I and Case II, respectively) which are matched to a particular predominant natural vibration period in accordance with the time period window resulting from a frequency analysis, as well as the natural period computed according to Eurocode 8 guidance. In addition, to replicate a real earthquake situation as accurately as possible, two types of excitation are applied, including unidirectional and bidirectional excitations for the different natural periods. Eurocode 8 requires that structures remain operational following relatively frequent earthquake events without incurring significant damage and incurring no structural damage. As such, the code defines an acceptable degree of reliability and validity for acceptable damage which must be reviewed during the design stage. The storey drift criterion is one of the primary stability criteria used in seismic codes and the Eurocode 8 limit is specified as 1% of the storey height under the ultimate design earthquake, which is 0.03 m in the present study.

In order to understand how an earthquake impacts upon a structure's fire resistance, a series of fire-only analyses are first presented. Figure 8 illustrates the collapse mechanism for a steel frame following a fire whilst Figure 9 shows the time-displacement and temperature-displacement curves, respectively, for the fire-only scenario. It is observed that local failure occurs concurrently for the two opposing beams in a symmetrical manner. The failure occurred around 260 sec after the fire began and at a temperature of approximately 480 ◦C.

The results from the PEF analysis for Case I, which involved an artificial earthquake, with a PGA of 0.35 g and a predominant natural vibration period of 0.16 sec, exposed to excitation in the Z direction, are presented in Figures 10 and 11. Figure 10 presents (a) the residual deformation that the steel frame experiences due to the earthquake excitation as well as (b) the shape and mechanism of failure of the structure (in the beam) after the PEF event for Case I. Whereas, Figure 11 presents the time-displacement results in the (a) z-direction, (b) y-direction and (c) the total displacement value respectively, as caused by PEF loading, as well as (d) temperature total displacement results due to PEF, for the case I scenario. The data from the corresponding fire-only analysis is also provided in these images.

**Figure 8.** Failure mechanism (Fire-only scenario).

**Figure 9.** *Cont.*

**-0.15**

**0 50 100 150 200 250 300 350 400**

**Time (sec)**

Fire-only scenario

Case I PEF scenario, Z direc.

**-0.1**

**-0.05**

**Displacement(m)**

**0**

**0.05**

**0.1**

**0.15**

**Figure 9.** Results from the fire-only analysis of the steel framed structure including (**a**) the time-mid-span displacement; (**b**) the temperature-mid-span displacement; (**c**) the time-mid-span displacement data for the total displacement, and (**d**) the temperature-mid-span displacement record for the total displacement.

**Figure 10.** Images from a Case I PEF analysis with an artificial earthquake (PGA = 0.35 g, natural period = 0.16 sec), one-directional excitation in the z-direction including (**a**) the residual deformation of the structure at the end of earthquake event and (**b**) the shape and mechanism of failure of the structure after the PEF event.

**-0.02**

**0 50 100 150 200 250 300 350 400**

Fire-only scenario Case I PEF scenario, Y direc.

**Time (sec)**

**-0.01**

**Displacement(m)**

**0**

**0.01**

**0.02**

**Figure 11.** Comparison of the fire-only analysis versus the PEF analysis for Case I including (**a**) the time-mid-span displacement record in the z-direction, (**b**) the time-mid-span displacement in the y-direction, (**c**) the time-mid-span displacement record for the total displacement and (**d**) the temperature-mid-span displacement record for the total displacement.

The results indicate that the structure maintains the earthquake force successfully, experiencing geometrical and mechanical damage within the acceptable range of Eurocode 8. However, in comparison with the images for the fire-only scenario provided in Figure 10, it is clear that the failure shape in the PEF case is no longer symmetrical. In addition, the collapse occurs after just 272 sec, which is a 19% reduction from the fire-only case, and at a temperature of 455 ◦C. The storey drift value at collapse is 0.024 m and therefore remains within the 0.03 m limit stipulated by Eurocode 8. The corresponding results for the Case II scenario (PGA of 0.35 g and a natural period of 0.36 sec) are presented in Figures 12 and 13, respectively. It is clear that the failure mechanisms are unsymmetrical, and in this case, collapse occurs after 278 sec and at a temperature of 458 ◦C, which is almost identical to Case I.

The data presented for both Case I and Case II reflect the effect of an earthquake on the fire strength of the structure during unidirectional excitation. This kind of the excitation does not represent the situation of earthquake excitation in reality, which is also typically unidirectional. Due to this, more observations are obtained by examining the structural response to bidirectional excitation for a further two real and artificial motions (Cases III and IV, respectively).

**0**

**0 50 100 150 200 250 300 350 400**

Fire-only scenario Case I PEF scenario, Mag.

**Time (sec)**

**0.05**

**0.1**

**Displacement(m)**

**0.15**

**0.2**

**0**

**0 50 100 150 200 250 300 350 400 450 500**

Fire-only scenario Case I PEF scenario, Mag.

**Temperature (°C)**

**0.04**

**0.08**

**Displacement (m)**

**0.12**

**0.16**

**Figure 12.** Images from a Case II PEF analysis with a real earthquake (PGA = 0.35 g, natural period = 0.36 sec) one-directional excitation in the z-direction, including (**a**) the residual deformation of the structure at the end of earthquake event and (**b**) the shape and mechanism of failure of the structure after the PEF event.

Figures 14 and 15 present the results from the analysis of a Case I earthquake with bidirectional excitation in both the x- and z-directions (referred to as Case III); these figures are presented in a similar format as before, for the purpose of comparison. It is clear that the global failure mechanism is dominant due to the combined effects of bidirectional excitation and the PEF event. The columns of one side of the structure completely collapsed in this scenario. The displacement records at a level of 1.4 m along the column length, for both the fire-only and PEF events are compared in Figure 16, which presents the time-mid-span displacement results at this position in (a) the x-direction, (b) the y-direction and (c) of the total displacement, respectively. Figure 16d presents the temperature-displacement response at the same point, 1.4 m from the column base. For this case, with bidirectional excitation, failure occurred after just 185 sec and at a temperature of 306 ◦C, representing a reduction of 45% compared with the fire-only analysis. The storey drift was 0.118 m, exceeding the allowable Eurocode 8 value. Similar behaviour and results are observed for Case IV, which has an identical input motion as Case II except with bidirectional excitation in both the x- and z-directions. The corresponding results are provided in Figures 17–19, in a similar format as before. It is clear that there is a significant reduction in the failure time for the PEF situation in Case IV of approximately 45% (to 185 sec) as well as a storey drift of 0.115 m, exceeding the allowable Eurocode 8 limit value by 85%. Significant local and global failure occurs in this case, preventing the structure from withstanding the applied loads.

**Figure 13.** Comparison of the fire-only analysis versus the PEF analysis for Case II including (**a**) the time-mid-span displacement record in the z-direction, (**b**) the time-mid-span displacement in the y-direction, (**c**) the time-mid-span displacement record for the total displacement and (**d**) the temperature-mid-span displacement record for the total displacement.

In this section, a detailed numerical investigation into the behaviour of a steel-framed subject to a PEF event is presented. Structural damage, residual deformation, and stress degradation as result of earthquake excitation are considered and included in the multihazard analysis. Two different types of structural failure due to the effect of the combined hazards are observed, namely local and global failure. The failure times for all of the analysed cases are compared to the corresponding values from a fire-only analysis in Figures 9, 11, 13, 15, 16 and 18. In addition, Figure 20 presents a comparison of the fire-only analysis versus the PEF analysis for each of the four analysed cases (I–IV). It is shown that the geometrical and mechanical damage induced by an earthquake event can substantially decrease the fire resistance of the structure, specifically in the occurrence of bidirectional excitation (see Table 2). This observation has a significant consequence on the design aspects of the system for multi-hazard analysis. The design load combination, the number of structural modes incorporated in the seismic design as part of the multi-hazard investigation and the structural element section type are very influential parameters. Although the current study has not included a detailed investigation of the effects of different cross-section shapes, specifically tubular members, the results presented provide a valuable insight into the significant effects of a PEF event on a steel framed structure, and also on the importance of choosing a suitable column section in earthquake-prone zones. Furthermore, based on these results, it is proposed that using tubular sections is essential in earthquake zones to provide extra resistance in a PEF scenario, even though

**0.15**

other sections may satisfy the seismic design requirements (that do not consider PEF). This is clearly an area that requires further research. Further, the load combinations provided in international codes do not currently include provisions for post-earthquake fire and each event is considered completely independently. The results presented herein do not support such an approach.

**Figure 14.** Images from a Case III PEF analysis with a real earthquake (PGA = 0.35 g, natural period = 0.24 sec), bi-directional excitation in the x- and z-direction including (**a**) the residual deformation of the structure at the end of earthquake event and (**b**) the shape and mechanism of failure of the structure after the PEF event.

**0.2**

**Figure 15.** *Cont.*

**Displacement(m)**

**Displacement(m)**

**Figure 15.** Comparison of the fire-only analysis versus the PEF analysis for Case III including (**a**) the time-mid-span displacement record in the z-direction, (**b**) the time-mid-span displacement record in the x-direction, (**c**) the time-midspan displacement record for the total displacement and (**d**) the temperature-mid-span displacement record for the total displacement.

**Figure 16.** Comparison of the displacement values at a point which is 1.4 m along the column length for both the fire-only and PEF events for Case III including (**a**) the time-displacement record in the x-direction, (**b**) the time-displacement record in the y-direction, (**c**) the time-displacement record for total displacement value and (**d**) the temperature-displacement record for the total displacement value.

**Temperature (°C)**

**Time (sec)**

**Figure 17.** Images from a Case IV PEF analysis with an artificial earthquake (PGA = 0.35 g, natural period = 0.16 sec), bi-directional excitation in the x- and z-direction including (**a**) the residual deformation of the structure at the end of earthquake event and (**b**) the shape and mechanism of failure of the structure after the PEF event.

**Figure 18.** *Cont.*

**Displacement(m)**

**Displacement(m)**

**Figure 18.** Comparison of the fire-only analysis versus the PEF analysis for Case IV including (**a**) the time-mid-span displacement record in the y-direction, (**b**) the time-mid-span displacement record in the z-direction, (**c**) the time-midspan displacement record for the total displacement and (**d**) the temperature-mid-span displacement record for the total displacement.

**Time (sec) Temperature (°C) Figure 19.** Comparison of the displacement values at a point which is 1.4 m along the column length for both the fire-only and PEF events for Case IV including (**a**) the time-displacement record in the y-direction, (**b**) the time-displacement record in the z-direction, (**c**) the time-displacement record for total displacement value and (**d**) the temperature-displacement record for the total displacement value.

**Figure 20.** Comparison of the fire-only analysis versus the PEF analysis for the time -temperature response including (**a**) case I, (**b**) case II, (**c**) case III and (**d**) case IV.


**Table 2.** Results comparison for all analysed circumstances.

#### **6. Conclusions**

This paper presents a detailed analysis of the influence of a post-earthquake fire on the behaviour of a steel framed building. It is clear that there are grave consequences in terms of occupant and structural safety during this type of multi-hazard scenario. Therefore, an accurate analysis of the response of structures exposed to such an event is required at the design stage, especially for very important buildings. The likelihood of a fire occurring following an earthquake is reasonably high, despite PEF being the subject of relatively little research in the available literature. In most design codes, structures exposed to multiple hazards such as earthquakes and then fires are analysed and designed separately. Structures subjected to an earthquake experience partial damage, and the subsequent occurrence of a fire may lead to structural collapse. Most available analysis procedures and design codes do not address the association of the two hazards. Thus, the design of structures based on existing standards may present a high risk of structural failure.

A suitable method of analysis has been developed in this paper to investigate the behaviour of structures that are exposed to such sequential hazards. Investigating the effects

of PEF on structures classified as "ordinary" in the design codes (such as educational and residential buildings, for example) is necessary as these types of building are very common in urban and well-populated environments. A performance-based design consideration requires structures to remain within the 'life safety' level of response under the design for the occurrence of an earthquake and fire, separately. In the current paper, two types of failure mechanisms are detected for steel framed buildings subjected to PEF—global and local failure. Local failure happens in the beams, whereas global failure is evidenced by significant lateral movement in the columns due to bidirectional excitation. Interestingly, the majority of the fire-only analyses discussed herein resulted only in a local collapse, while all of the PEF analyses with bidirectional excitation resulted in a global collapse. Therefore, it is clear that the failure mode for a PEF can be quite different compared to a single hazard event. Consequently, it is suggested that columns with greater bi-directional stiffness (e.g., tubular sections) are likely to offer the greatest ultimate resistance in earthquake hazard zones under the combined effects of bidirectional earthquake excitation and subsequent fire. Despite the investigations in this paper being performed in relation to a particular class of structures, the results confirm the need to incorporate PEF as a load case during both the analysis and design stages. Further studies need to be performed either numerically or experimentally, using complete a seismic soil-structure interaction analysis, to develop a better understanding of the issue.

**Author Contributions:** Conceptualization, A.T.A. and P.E.F.C.; Methodology, A.T.A. and K.A.C.; Software, A.T.A.; Validation, A.T.A., P.E.F.C. and K.A.C.; Formal analysis, A.T.A.; Investigation, A.T.A.; Data curation, A.T.A., P.E.F.C. and K.A.C.; Writing—original draft preparation, A.T.A.; Writing—review and editing, P.E.F.C. and K.A.C.; Visualization, A.T.A.; supervision, P.E.F.C. and K.A.C.; project administration, P.E.F.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The study did not report any data.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Parametric Analysis of a Steel Frame under Fire Loading Using Monte Carlo Simulation**

**Ragad Almadani and Feng Fu \***

School of Mathematics, Computer Science and Engineering, City, University of London, London EC1V 0HB, UK; raghad.almadani.19@ucl.ac.uk

**\*** Correspondence: feng.fu.1@city.ac.uk

**Abstract:** In this paper, the parametric analysis of the thermal and structural response of a two-storey, single-zone steel frame building on fire is made considering different parameters Monte Carlo simulation is used to generate random variables for the opening factor, fire compartment area and finally the beam flange thickness. Using the random parameter generated, a sequential thermal and mechanical analysis was conducted using the finite element software ABAQUS. The first step was a heat transfer analysis, followed by mechanical analysis. The effect of different parameters on the thermal and mechanical response of the structure was studied.

**Keywords:** City University; fire temperature; opening factor; compartment area; thermal analysis

#### **1. Introduction**

Steel has been the forefront of efficient construction in the last few years, where it has been used widely in the construction of high-rise buildings, industrial structures and residential structures. What makes steel one of the most appealing materials in the construction industry is its engineering properties. The most appealing properties of steel are its strength to weight ratio, ductility and flexibility. Such properties allow designers to build structures such as skyscrapers, which certainly would have not been possible with any other material. Steel can also be prefabricated and shipped to construction sites easily, which is quite beneficial when it comes to meeting the ever-increasing demands of new buildings. Nevertheless, there is a huge downside to using steel as a construction material because of its low resistance to fire when compared to other construction materials such as concrete. Steel loses almost half of its strength when subjected to temperature which is equal to or greater than 590 ◦C, which will eventually lead the structure to fail. The losses that follow structural failures caused by fire are colossal and can take different forms, such as loss of human lives, environmental loss and economical loss. Hence, the insurance of structural stability of a building under fire loading has been one of the most important and challenging aspects when it comes to designing a new structure [1]. It is important that in the event of a fire, structures are able to withstand the minimum level of life safety not only for the occupants but also fire fighters and the public that are in proximity of the building. The minimum level of fire safety design must ensure a reduction of the risk of deaths and injuries, protect the contents of a building, and ensure that the building continue to function after the fire with the least amount of repair possible.

In order to ensure that the structure meets the fire safety design objectives, designers have to follow one of two methods; the first is the prescriptive method, where a detailed description of the types and shapes of materials used in the design, the thickness of protection layer on structural elements and even the details of construction are given. However, this method relies solely on previous experience of the standard structural fire design tests. While this approach is very useful when it comes to static situations, it sometimes fails to meet the fire safety requirements of a building, raising concerns about the limitations of this method. One of its limitations is that the standard structural fire

**Citation:** Almadani, R.; Fu, F. Parametric Analysis of a Steel Frame under Fire Loading Using Monte Carlo Simulation. *Fire* **2022**, *5*, 25. https://doi.org/10.3390/fire5010025

Academic Editor: Maged A. Youssef

Received: 28 December 2021 Accepted: 9 February 2022 Published: 14 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

design tests assume that the structural elements of a building work independently, which is not the case in reality [2,3]. This approach is usually used for quick solutions and for junior designers, because it does not require an in-depth knowledge of the field.

The second method is the performance-based approach, which indicates how a structure will perform when subjected to different load conditions. Designers who use this method need to develop an accurate numerical simulation for fire loading to assess the fire safety resistance of the structure [4–7]. There are three main components to this approach: fire modelling, thermal analysis and structural analysis [2,3]. Keeping this in mind, this method allows designers to come up with solutions to build complex structures that were never possible with a standard prescriptive approach. This approach is usually adopted for more optimum solutions that require computational skills and deep understanding of the field.

There are a number of different modelling techniques commonly used today to predict the different fire scenarios instead of carrying out experimental tests. The techniques used range from simple hand calculations to more advanced computational techniques. Deciding which technique to use depends on the level of accuracy needed for the project, time restrictions and computational resources. With the development of software packages, designers can use a number of methods to predict possible fire scenarios in a building in order to further control the risk of a fire event. Some of these methods include zone models, computational fluid dynamics (CFD) [8] models and finite element (FE) models [9]. Zone models are simple computational models that operate on the basis of dividing a compartment area into separate zones, with the assumption that the temperature condition is uniform throughout each zone. CFD models are more sophisticated than zone models, because they analyze the fluid flow and heat transfer by solving the fundamental equations of fluid dynamics. Finally, FE models operate by dividing a large geometry into several hundred smaller parts that interact with each other. Given the different methods designers can adopt to predict the different fire scenarios, the uncertain nature of the different factors affecting a fire event the structural stability of a building one of the most challenging responsibilities for structural engineers. The fuel, load density and ventilation areas are all factors that contribute to a fire event and its duration. Moreover, the unpredictable nature of the response of structural elements to fire makes the whole fire process stochastic. As a result, the engineering design of structural fire is either based on empirical studies of the behavior of fire or on reliability analysis [10].

The FE modelling technique is one of the most straightforward methods used to predict the thermal and structural behavior of the structural members, according to [4–7]. The simulation works by breaking up large geometry to hundreds of smaller and simpler parts that interact together. In order to run the simulation using the finite element modelling technique, the thermal and mechanical properties of the material used in construction have to be calculated according to design codes. Design codes such as Eurocode provide formulas to calculate the thermal properties of a material and curves to obtain gas temperatures. The values obtained from the formulas provided can then be applied directly to the model using software packages.

However, most variables used during the fire analysis are either estimated or assumed, which makes the efficiency of the design in doubt and highlights the importance of the concept of intensive parametric study in structural fire design. As in reality, the parameters vary due to different fire scenarios; to effectively study the influence of different parameters, one of the promising methods is the Monte Carlo simulation [11]. This method generates hundreds of random variables for the different stochastic parameters that relate to fire, which allow designers to analyze the buildings under different fire scenarios, and thus to maximize the reliability and safety of the design.

Therefore, in this paper, the parametric analysis of the thermal and structural response of a two-story, single-zone steel frame building to fire is made considering different parameters; Monte Carlo simulation is used to generate random variables for the opening factor, fire compartment area and the beam flange thickness. Using the random parameters

generated, a sequential thermal and mechanical analysis was conducted using the finite element software ABAQUS. The first step was a non-linear heat transfer analysis, followed by a non-linear mechanical analysis. The effect of different parameters on the thermal and mechanical response of the structure was studied.

#### **2. Monte Carlo Simulation**

The Monte Carlo Simulation is used here to generate the random parameters which will affect the fire scenarios and the thermal response of the structural steel members in a steel framed building. The key factors affecting the fire scenarios and thermal response of a structure under fire conditions are explained here

#### *2.1. Time-Temperature Curves for a Compartment*

The room temperature of a building in fire can be calculated using the formulas from Eurocode, BS EN 1993-1-2: Eurocode 1 part 1.2 [12] which gives the parametric time temperature of a compartment in fire:

$$\Theta\_{\mathcal{S}} = 20 + 1325 \left( 1 - 0.324 \, e^{-0.2t^\*} - 0.204 e^{-1.7t^\*} - 0.472 e^{-19t^\*} \right) \tag{1}$$

With

$$\mathbf{t}^\* = \mathbf{t} \times \Gamma \tag{2}$$

$$
\Gamma = [\text{O/b}]^2 / (0.04/1160)^2 \tag{3}
$$

$$\mathbf{O} = \mathbf{A}\_{\mathbf{v}} \sqrt{h\_{\text{eq}}} / \mathbf{A}\_{\mathbf{t}} \tag{4}$$

$$\mathbf{b} = \sqrt{(\rho c \lambda)}\tag{5}$$

where θ*<sup>g</sup>* is the gas temperature in the fire compartment (◦C), t is the time (m), O is the opening factor (m1/2), b is the thermal diffusivity (J/m<sup>2</sup> s 1/2 K), *ρ* is the density (kg/m<sup>3</sup> ), C is the specific heat (J/kgK), λ is the thermal conductivity (W/mK), A<sup>t</sup> is the total internal surface area of the compartment (m<sup>2</sup> ), A<sup>v</sup> is the area of ventilation (m<sup>2</sup> ) and heq is the height of openings (m) [12,13].

#### *2.2. Thermal Response of Structural Members*

For unprotected steel sections, the increase of temperature in a small time interval is given by BS EN 1993-1-2: Eurocode 3 [13] as follows:

$$
\Delta\theta\_{a,t} = k\_{sh}\frac{\mathbf{A\_m}/\mathbf{V}}{c\_a\rho\_a}\dot{h}\_{net}\Delta t\tag{6}
$$

where, ∆*θa*,*<sup>t</sup>* is the increase of temperature. Am/V is the section factor for unprotected steel member. A<sup>m</sup> is the exposed surface area of the member per unit length. V is the volume if the member per unit length. *c<sup>a</sup>* is the specific heat of steel. *ρ<sup>a</sup>* is density of the steel.

#### *2.3. Monte Carlo Simulation*

Based on above formulas from the design code, three main parameters dominate the room temperature and thermal response of the structural member. They are the opening factor (O), the compartment area (Acom) and the cross-sectional area of the structural members (Am). Therefore, in the Monte Carlo simulation, the opening factor (O), the compartment area (Acom) and the thickness of the flange for the steel I-section beam were selected as the key parameters for the random simulation. These three parameters were selected based on Equations (1) and (3), since these three parameters play important roles in determining the thermal response of the structural members. The Monte Carlo simulation code was developed using MATLAB [11]. The code developed uses an inbuilt command called 'normrnd' to generate normal random numbers between the specified range to form a set of inputs that generate the different fire scenarios. The specified limits for the opening factor (O) and the compartment area (Acom) were set according to the British Standard Institutes [12], and the limits for the flange thickness of the I-beam section were chosen according to the British Standard Institutes [12,13], as shown in Table 1. The number of simulations chosen was 500, which is believed to be sufficent to produce reasonable parameters in a real fire scenario.


**Table 1.** Range of the parameters used for Monte Carlo simulation.

The MATLAB code generated 500 random numbers for each parameter. Amongst the 500, only five numbers were chosen in this paper. These values are tabulated in Table 2.


**Table 2.** Chosen values from the Monte Carlo simulation.

The values noted above were used to run the heat transfer analysis in Section 3. The corresponding unique nodal temperatures were extracted for all cases and used to run the mechanical analysis explained in Section 3.

#### **3. Finite Element Analysis**

#### *3.1. Finite Element Model*

The finite element analysis procedure was split into two stages: (1) Heat Transfer Analysis and (2) Mechanical Analysis. The FE model is a two-story, one-bay by one-bay steel frame structure. Each story is 3 m high, making the whole structure 6 m high in total and 7 m by 5.5 m in width. This is a typical steel frame office dimension, according to (Tagawa et al., 2015). Different element types have been tried in order to choose the suitable element to simulate the behavior of the composite connections. 3D continuum elements were used. C3D8R element with reduced integration (1 Gauss point) has been chosen for the simulation of all the components in the model. The model simulates a corner fire with a three hour duration. Due to time constrictions, only the steel frame was modelled without the slab. ABAQUS was used for both simulations.

#### *3.2. Heat Transfer Analysis*

In order to construct the two-story steel frame structure on ABAQUS, three main parts were created: a 6 m column, 5.5 m and 7 m beams, and a partitioned midway. The values of the steel's conductivity (λa), steel's specific heat (Ca) and steel's density (ρa) were obtained from Eurocode. All three parts were assigned the same steel material. Furthermore, an instance was created and the three different parts were added in order to assemble the elements as one whole structure. This was done with the use of the offset, rotate and translate commands.

After that, a heat transfer step was created with a time period of 10,800 s, and the maximum increment per step was set to 10. Before simulating the heat transfer analysis, an amplitude of the gas temperature was obtained from Equation (1) for simulating the different fire scenarios using the parameters generated from the Monte Carlo simulations.

ABAQUS will fail to run any heat transfer analyses if the absolute zero temperature and Stefan-Boltzmann constant (σ) were not inputted. Hence, from model attributes, a value of <sup>−</sup>273.5 was given to the former and a value of 5.67 <sup>×</sup> <sup>10</sup>−<sup>8</sup> to the latter. Before the analysis was submitted for results, the entire structure was meshed using hexagonal element shapes and assigned an element type of heat transfer. After the analysis was submitted, and the heat analysis results were completed, the unique nodal temperatures at three different locations were extracted and the average value was taken in order to apply them at the heat load analysis stage.

For the convergence criterion, the default solution control parameters defined in ABAQUS/Standard are designed to provide reasonably optimal solutions of complex problems involving combinations of nonlinearities as well as efficient solutions of simpler nonlinear cases. However, the most important consideration in the choice of the control parameters is that any solution accepted as "converged" is a close approximation to the exact solution of the nonlinear equations. In this context "close approximation" is interpreted rather strictly by engineering standards when the default value is used, as described below.

#### *3.3. Mechanical Analysis*

The mechanical analysis was subsequently carried out using ABAQUS. The true stress-strain curve was used for the material model of the steel. The most relevant mechanical properties for this model are the yield stress (σy), plastic strain (εp), expansion Co-efficient (α), young's modulus (E) and Poisson's ratio (ν). Thereafter, a solid homogeneous section was created with the new material, which was then assigned to the three different parts.

Following that, a step from the general static type was created, with a time period of 10,800 s, and the maximum number of increments was set to 1000, initial of 10, minimum of 0.108 and maximum of 60. The next step was to create a boundary condition for the fixed supports of the steel frame and apply the gravity load (dead and live loads) to the entire structure; this was done directly from the model tree.

Before the load was applied, the unique nodal temperature obtained from the heat transfer analysis was used to create an amplitude. The temperature on each node from the heat transferring analysis step was added through a predefined field; hence, a predefined field of the type 'temperature' was then created, and the relevant parts of the geometry were selected in order to simulate the same corner fire from the previous step. This was to simulate the corner fire test from the Cardington fire test, which is believed to be the worst-case scenario for a building on fire. The magnitude of the predefined field was set to 1 and the amplitude to the one created using the unique nodal temperatures from the heat transfer analysis.

For this type of analysis, the software for the normal hexagonal elements type was first used for meshing the structure; however, due to the complexity of the geometry of the structure, the assembly could not be meshed properly. Instead, the structure was meshed using the tetrahedral elements type. About 10 different mesh sizes were tried before a final mesh size was determined. This was done through assigning different seeds in the mesh module in ABAQUS, and ABAQUS generated the mesh automatically. Finally, a job was created and submitted; the energy results were then viewed, and the values for the displacement of the beams in all x, y and z directions were extracted.

#### **4. Parametric Analysis**

#### *4.1. Effect of Opening Factor*

The first set of results were obtained from both finite element analyses: (1) Heat transfer analysis, and (2) heat load analysis corresponded to the different opening factors obtained from the Monte Carlo simulation (Table 2). The different opening factors were applied to a steel frame with fixed dimensions (5.5 × 7 m) in terms of temperature amplitudes The results of the heat transfer load are shown in the form of nodal temperatures (NT11), whereas the results obtained from the mechanical analysis are shown in the form of displacement (U).

• **Scenario 1**: An opening factor with a value of 0.0251 was used, and the corresponding results are shown in Figure 1a,b.

**Figure 1.** Effect of opening factors. (**a**) The nodal temperature corresponding to the opening factor of 0.0251. (**b**) The displacement corresponding to the opening factor of 0.0251.

• **Scenario 2**: An opening factor with a value of 0.0554 was used, and the corresponding results are shown in Figure 2a,b.

**Figure 2.** Effect of opening factors. (**a**) The nodal temperature corresponding to the opening factor of 0.0554. (**b**) The displacement corresponding to the opening factor of 0.0554.

• **Scenario 3**: An opening factor with a value of 0.1129 was used, and the corresponding results are shown in Figure 3a,b.

**Figure 3.** Effect of opening factors. (**a**) The nodal temperature corresponding to the opening factor of 0.1129. (**b**) The displacement corresponding to the opening factor of 0.1129.

 (**a**) (**b**)

**Figure 4.** Effect of opening factors. (**a**) The nodal temperature corresponding to the opening factor of 0.1961. (**b**) The displacement corresponding to the opening factor of 0.1961.

• **Scenario 5**: An opening factor with a value of 0.1961 was used, and the corresponding results are shown in Figure 5a,b.

**Figure 5.** Effect of opening factors. (**a**) The nodal temperature corresponding to the opening factor of 0.0554. (**b**) The displacement corresponding to the opening factor of 0.0554.

#### *4.2. Effect of Compartment Area*

The second set of results shown in this section represent the finite element analyses that correspond to the different compartment area dimensions (Table 2). While the dimension of the plan of the steel frame changed, the temperature amplitude and heat load remained constant. In order to achieve the desired compartment area size, one of the beams was given a fixed length of 7 m, while the other beam changes with every scenario. The results are represented below in the form of NT11 and U for each scenario generated by the Monte Carlo simulation.

• **Scenario 1**: A compartment area with a size of 32.9 m<sup>2</sup> was modelled, and the beam lengths were 7 and 4.7 m in length. The corresponding results are shown in Figure 6a,b.

**Figure 6.** Effect of Compartment Area. (**a**) The nodal temperature corresponding to the compartment area of 32.9 m<sup>2</sup> . (**b**) The displacement corresponding to compartment area of 32.9 m<sup>2</sup> .

• **Scenario 4:** An opening factor with a value of 0.1689 was used, and the corresponding results are shown in Figure 4a,b.

• **Scenario 2**: A compartment area with a size of 42 m<sup>2</sup> was modelled, and the beams were 7 and 6 m long. The corresponding results are shown in Figure 7a,b.

**Figure 7.** Effect of Compartment Area. (**a**)The nodal temperature corresponding to the compartment area of 42 m<sup>2</sup> . (**b**) The displacement corresponding to the compartment area of 42 m<sup>2</sup> .

• **Scenario 3**: A compartment area with a size of 56 m<sup>2</sup> was modelled, and the beams were 7 and 8 m long. The corresponding results are shown in Figure 8a,b.

**Figure 8.** Effect of Compartment Area. (**a**) The nodal temperature corresponding to the compartment area of 56 m<sup>2</sup> . (**b**) The displacement corresponding to the compartment area of 56 m<sup>2</sup> .

• **Scenario 4:** A compartment area with a size of 70 m<sup>2</sup> was modelled, and the beams were 7 and 10 m long. The corresponding results are shown in Figure 9a,b.

**Figure 9.** Effect of Compartment Area. (**a**) The nodal temperature corresponding to compartment area of 70 m<sup>2</sup> . (**b**) The displacement corresponding to to compartment area of 70 m<sup>2</sup> .

• **Scenario 5:** A compartment area with a size of 79.8 m<sup>2</sup> was modelled, and the beams were 7 and 11.4 m long. The corresponding results are shown in Figure 10a,b.

**Figure 10.** Effect of Compartment Area. (**a**) The nodal temperature corresponding to the compartment area of 79.8 m<sup>2</sup> . (**b**) The displacement corresponding to the compartment area of 79.8 m<sup>2</sup> .

#### *4.3. Effect of Flange Thickness*

The third and last set of results represented in this section are related to the beam flange thickness. The thickness of the flange varied from 7.9 to 25.8 mm while the dimensions of the steel frame including the beams webs were fixed. The temperature amplitude and heat load applied to the structures were also fixed. The results represented are in the form of NT11 and U.

• **Scenario 1**: The thickness of the flange was set to 7.9 mm, and the corresponding results are shown in Figure 11a,b.

**Figure 11.** Effect of flange thickness. (**a**) The nodal temperature corresponding to the flange thickness of 7.9 mm. (**b**) The displacement corresponding to the flange thickness of 7.9 mm.

• **Scenario 2**: The thickness of the flange was set to 9.3 mm, and the corresponding results are shown in Figure 12a,b.

**Figure 12.** Effect of flange thickness. (**a**) The nodal temperature corresponding to flange thickness of 9.3 mm. (**b**) The displacement corresponding to flange thickness of 9.3 mm.

• **Scenario 3**: The thickness of the flange was set to 16.7 mm, and the corresponding results are shown in Figure 13a,b.

**Figure 13.** Effect of flange thickness. (**a**) The nodal temperature corresponding to flange thickness of 16.7 mm. (**b**) The displacement corresponding to flange thickness of 16.7 mm.

• **Scenario 4:** The beam flange thickness was set to 19.3 mm, and the corresponding results are shown in Figure 14a,b.

**Figure 14.** Effect of flange thickness. (**a**) The nodal temperature corresponding to flange thickness of 19.3 mm. (**b**) The displacement corresponding to flange thickness of 19.3 mm.

• **Scenario 5:** The beam flange thickness was set to 25.8 mm, and the corresponding results are shown in Figure 15a,b.

**Figure 15.** Effect of flange thickness. (**a**) The nodal temperature corresponding to flange thickness of 25.8 mm. (**b**) The displacement corresponding to flange thickness of 25.8 mm.

#### *4.4. Summary*

From the parametric temperature-time curve Equation (1), it is clear to see that the opening factor plays an important role when it comes to determining the spread time of the fire along with the gas temperature increase in the fire compartment. Therefore, when looking at the gas temperature curves obtained from the different opening factors, it can be observed that the larger the opening factor is, the higher the gas temperature will be. The highest opening factor reaches the highest temperature in the shortest time. In fact, the highest gas temperature reached was by the largest opening factor, around 1300 ◦C. This is almost twice as much as the maximum gas temperature reached by the smallest opening

factor, which was around 800 ◦C. However, the maximum specified limit of opening factor by Eurocode is 0.2.

From the ABAQUS model, it can be also seen that with different opening factors, the regions with the highest nodal temperatures were the upper flanges of both the beams and the inner web of the column, which was expected due to the fact that the load in both analyses was applied in those regions. The highest observed nodal temperature was found to be 1347 ◦C, corresponding to the opening factor of 0.1961; similar results were obtained for the opening factor of 0.1689, where it was around 1343 ◦C. On the other hand, the lowest observed temperature was found when the opening factor was 0.0251, where the temperature only reached 838.6 ◦C. When compared to the recorded temperatures from the Cardington tests [5], the temperatures from the numerical analysis are higher. In fact, the maximum nodal temperatures observed here are almost the same as the gas temperatures reached. This is mainly due to the fact that the steel was designed to be unprotected and there were no slabs modelled. Thus, the upper flange of the beam has a hotter temperature because it is in direct contact with the gas temperature.

The maximum displacement in the y-direction was plotted for the different opening factors as shown in Figure 16. In general, all beams started to deflect at around the same time; however, the highest deflection recorded was associated with the one of the highest opening factors (O = 0.1689), where it reached to around 0.014 m.

**Figure 16.** Beam displacement in the y-direction corresponding to the different opening factors.

The results of the displacement in the y-direction for the different compartment areas are plotted in Figure 17. The plot shows that the highest deflection recorded was for the area of 70 m<sup>2</sup> , and it was around 0.014 m. It was also noted that in general there were around two general trends followed: one was followed by the plots corresponding to both 32.9 and 70 m<sup>2</sup> , and the other one followed by the remaining three. However, the latter curves started to deflect quicker than the former. The reason for this could be the fact that the results extracted from the model were chosen at random, even though an average of value was taken from three different nodes to minimize errors.

> A=32.9 A=42 A=56 A=70 A=79.8

0 50 100 150 200

Time, t (s)

0

0.002

0.004

0.006

0.008

Displacement, U (m)

0.01

0.012

0.014

0.016

0 50 100 150 200

O=0.0251

O=0.0554

O=0.0112 9

Time, t (m)

0

0.002

0.004

0.006

0.008

Displacement, U (m)

0.01

0.012

0.014

0.016

The displacement in the y-direction corresponding to the different flange thickness are plotted in Figure 18. From the figure, it can be said that the beams with the thinner flange thickness deflected quicker than the thicker flanges, which can be explained by the amount of time it takes for the heat to radiate from the top flange to the bottom one.

From all scenarios, it can be observed that the general behavior of the beam is similar, despite the different factors affecting the final result. This is not surprising because in some cases the heat load applied or the compartment area was fixed.. From the general displaced shapes for all cases, shown in Section 4, it is safe to say that the expansion co-efficient of steel had the most influence when it comes to heat load, even though it was also observed that some of the results are exaggerated in some cases, such as the nodal temperatures; this is mainly due to the absence of the slab.

As explained in [14], the tortional restraint is very important for the bare steel beams. It should be modeled in the ABAQUS model, but in reality, the beams are restrained directly by the slabs, which actually help to resist the lateral tortional buckling of the beam. We did not model the lateral restraint so as to provide a worst-case scenario for the study. The fire protection is an important factor affecting the global and local response of a structure

on fire, but in this study, non-fire protection is assumed; this also provided a worst-case scenario for the study.

As explained in [15,16], the joints play an important role in the local and global behavior of the structure, as the moment and rotation capacity of the joints will affect the response of the structure. Therefore, the most accurate way to assess the joints is to physically model the bolts and endplate. Attempts have been made by the authors, but for a 3D frame system, the modeling of the bolted connection causes a convergence problem in the model, due to the complexity of the frame. Therefore, the beams are directly tied to the columns to replicate a perfect rigid connection, to reduce the computational cost while remaining reasonably accurate.

A further study will be performed by the authors to address the above limitations.

#### **5. Conclusions**

The aim of this project was to apply a parametric study of a steel frame in fire through sequential thermal and mechanical analyses. A two-story steel frame structure was simulated to investigate the influence of the opening factor, compartment area, and beam flange thickness using a Monte Carlo simulation to generate the random parameters. The following conclusions can be made:


**Author Contributions:** Conceptualization, F.F. Investigation, R.A. and F.F.; Methodology, F.F.; Supervision, F.F.; original draft, R.A.; Writing—review & editing, F.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**


#### **References**


## *Article* **Numerical and Experimental Analysis of Fire Resistance for Steel Structures of Ships and Offshore Platforms**

**Marina Gravit and Daria Shabunina \***

Peter the Great St. Petersburg Polytechnic University, 195251 St. Petersburg, Russia; marina.gravit@mail.ru

**\*** Correspondence: shabunina.de@edu.spbstu.ru

**Abstract:** The requirements for the fire resistance of steel structures of oil and gas facilities for transportation and production of hydrocarbons are considered (structures of tankers and offshore platforms). It is found that the requirements for the values of fire resistance of structures under hydrocarbon rather than standard fire conditions are given only for offshore stationary platforms. Experimental studies on the loss of integrity (E) and thermal insulating capacity (I) of steel bulkheads and deck with mineral wool under standard and hydrocarbon fire regimes are presented. Simulation of structure heating was performed, which showed a good correlation with the experimental results (convective heat transfer coefficients for bulkheads of class H: 50 W/m<sup>2</sup> ·K; for bulkheads of class A: 25 W/m<sup>2</sup> ·K). The consumption of mineral slabs and endothermic mat for the H-0 bulkhead is predicted. It is calculated that under a standard fire regime, mineral wool with a density of 80–100 kg/m<sup>2</sup> and a thickness of 40 to 85 mm should be used; under a hydrocarbon fire regime, mineral wool with a density above 100 kg/m<sup>2</sup> and a thickness of 60–150 mm is required. It is shown that to protect the structures of decks and bulkheads in a hydrocarbon fire regime, it is necessary to use 30–40% more thermal insulation and apply the highest density of fire-retardant material compared to the standard fire regime. Parameters of thermal conductivity and heat capacity of the applied flame retardant in the temperature range from 0 to 1000 ◦C were clarified.

**Keywords:** oil and gas facility; offshore platform; tanker; steel structure; bulkhead; deck; hydrocarbon fire mode; fire-resistance limit; fire protection

#### **1. Introduction**

Building structures of reservoirs, equipment and structures in an accident, accompanied by fire and explosion, are subjected to high-temperature impact due to the large number and type of fire load [1,2]. In Europe and the USA, combustion of hydrocarbons (oil, oil products) and the development of fire are considered on the hydrocarbon fire curve, at which, in the first minutes of the fire, the temperature reaches 1000 ◦C and higher [3,4]. In the design of structures of the oil and gas complex (O&G) in Russia, the condition of fire development on the standard ("cellulose") curve according to ISO 834 [5] is used.

Tankers are in second place in the total transportation volume of oil and petroleum products (after oil pipes). The highest risk of formation of explosive mixtures inside the tanker occurs during tanker unloading. When the liquid level drops, the air is exhausted into the tank and mixed with petroleum product vapors [6]. As petroleum vapors are heavier than air, they can spread through tanker rooms and ignite over large areas. Ships and offshore platforms consist of decks, compartments and interior spaces that contain several systems, subsystems and components necessary for operation. Explosion, fire or flooding of compartments can damage equipment and cause a critical risk to operations [7–9]. In [10], an empirical method was used to calculate the compressive strength limit in the center of the deck, according to the results of which, the maximum compressive stress on the deck was 175.53 MPa; the deflection value in the middle part of the deck did not exceed the acceptable value. In [11], the design of a working barge with a displacement of 5000 tons was

**Citation:** Gravit, M.; Shabunina, D. Numerical and Experimental Analysis of Fire Resistance for Steel Structures of Ships and Offshore Platforms. *Fire* **2022**, *5*, 9. https:// doi.org/10.3390/fire5010009

Academic Editor: Maged A. Youssef

Received: 19 December 2021 Accepted: 14 January 2022 Published: 16 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

demonstrated. Mechanical calculation showed sufficient strength under normal loading conditions and even in an emergency. In [12], the steel deck's behavior under different hydrocarbon ignition scenarios using ANSYS software was studied. Numerical studies of steel decks under the combined action of mechanical load and hydrocarbon fire regime are given, showing an increased deformation of the deck and reduced deck fire resistance under the considered fire scenarios. In [13,14], a fire was simulated using FDS structures of offshore platforms, and the fire risk was calculated. The authors investigated the behavior of steel structures of the upper part of an offshore platform under fire and hydrocarbon explosion and under wind load; the calculation was performed in ABAQUS software [15]. The thermophysical characteristics of the intumescent paints used as fire protection of steel structures were obtained in [16].

Steel structures in the ship's hull and structures of cargo tanks, decks and bulkheads that separate industrial rooms are designed with certain fire-resistance classes, depending on the parameters of the fire-resistance limits and temperature exposure modes: A, B, C and H (standard regime—A, B, C classes, and hydrocarbon—H class). The same fireresistance classes are established for oil platforms [17]. In [18], a simulation of the thermal impact on the steel structure A-60 was presented, from the results of which the temperature distribution was calculated. The analysis results allow consideration of the design and safety planning aspects of an offshore living compartment.

According to SOLAS Regulation II-2/17 [19], decks and bulkheads shall be made of non-combustible materials and are classified as follows:


Another classification of decks and bulkheads is also regulated in [17]:

(4) "H" class divisions: H-120, H-60 and H-0.

Figure 1 shows the location of the H-120 deck and A-60 and B-15 class bulkheads on the tanker.

**Figure 1.** (**a**) Tanker with H-120 deck location. (**b**) Fragment of the section of the first deck with the arrangement of the bulkheads.

Figure 2 shows the location of the H-120 deck and A-60 and H-120 class bulkheads on an offshore platform.

**Figure 2.** (**a**) Offshore platform with deck location. (**b**) Fragment of the section of the first deck with the arrangement of the bulkheads.

Fire-resistance tests of structures for ships and offshore structures are conducted following the requirements stated in SOLAS Regulation II-2/17 [19], International Maritime Organization (IMO) resolutions and guidelines of IMO member countries, for example, American Bureau of Shipping (ABS) [20] and Russian Maritime Register of Shipping (RS) [21]. Tests for fire resistance are carried out using both methods for determining the fire resistance of structures by the standard temperature regime (curves for A, B, C), which is similar to that established in ISO 834 [5], and by the hydrocarbon fire regime (curve H) for island structures and floating platforms. In the USA, the standard UL 1709 [22] is applied, which differs from the European EN 1363-2:1999 [23] in the development of a fire in the first minutes [24,25].

According to ISO 834-75 [5], IMO Res. A.754 [26] and the Russian State Standard GOST 30247.1 "Elements of building constructions. Fire-resistance test methods. Loadbearing and separating constructions" [27] harmonized with ISO 834 [5], the following limit conditions are distinguished for fire-resistance limits of enclosure structures, which include bulkheads and decks of tankers and platforms:


Minimum requirements for fire resistance of bulkheads and decks are established in [17,20,28], for example, for bulkheads in [17] (Table 1).


**Table 1.** Fire integrity of bulkheads separating adjacent spaces/areas.

Note: \* The division is to be of steel or equivalent material, but is not required to be of an A-class standard.

Insulation materials should generally be non-combustible or show low combustion spreading to ensure structural fire resistance of ships and platforms [29–31]. Mineral wool of various densities is widely used in passive fire protection (PFP) [32,33] and less commonly used in epoxy-based fire-retardant intumescent paints [4]. Fire protection is applied (mounted) between thin metal walls as bulkhead panels on vertical structural elements of offshore structures. Studies related to the design, calculation and modeling of decks and bulkheads include either only calculations of the compressive strength and deflection values at the center of the structure [10,11] or only modeling of hydrocarbon fire and explosion scenarios [12–15,18]. In [34], two experiments of bulkheads under standard and hydrocarbon fire regimes are given, with their subsequent modeling confirming the correlation of the obtained temperatures, from which the conclusion about the possibility of prediction and justification of the fire-resistance limits by simulation is made.

The purpose of this article is to simulate experimental data for determining the fireresistance limit of bulkheads of different classes and deck for an offshore platform to solve the following problems: calculation of the parameters of thermal insulation of bulkheads and deck; prediction of the fire-resistance limits of the structure on the example of the H-0 bulkhead depending on the thickness of mineral wool and its density for the H-0 bulkhead under a hydrocarbon fire regime with the variant to replace the used fire protection to endothermic mat based on ceramics and basalt fibers; calculation of the H-0 bulkhead on a deflection in the center of the considered structure under thermal load; and clarification of calculated coefficients of thermal conductivity and heat capacity for mineral wool in the temperature range from 0 to 1000 ◦C.

#### **2. Materials and Methods**

Experimental samples of H-class bulkheads and deck were tested to determine the time of reaching the limit state during fire exposure according to IMO FTP Code Part 3 IMO Res. A.754 (18) [26] under the condition of establishing a hydrocarbon temperature regime in the fire chamber of the furnace according to EN 1363-2: 1999 [23], characterized by dependence (1):

$$T - T\_0 = 1080 \times \left(1 - 0.325 \times e^{-0.167t} - 0.675 \times e^{-2.5t}\right) \tag{1}$$

where *T* means the temperature inside the furnace in ◦C, corresponding to the relevant time *t*; *T*<sup>0</sup> is the temperature in ◦C inside the furnace prior to the start of heat impact; *t* is the time in minutes from the start of the test.

Experimental samples of A-class bulkheads were tested to determine the time of reaching the limit state during fire exposure according to IMO FTP Code Part 3 IMO Res. A.754 (18) [26] under the condition of creating in the fire chamber of the furnace a standard temperature regime according to ISO 834 [5], characterized by dependence (2):

$$T - T\_0 = 345 \times \lg(8t + 1)\tag{2}$$

The furnace temperature was determined by means of twelve thermoelectric transducers with a switching head uniformly distributed at a distance of approximately 100 mm from the exposed side of the test sample according to IMO Res. A.754 (18) [26]. The temperature in the furnace during the fire tests was maintained according to the appropriate temperature regimes [23]. The temperature on the test samples was measured by cable thermoelectric chromel–alumel thermocouples. According to the test reports of the structure, each thermocouple is inserted through a steel pipe of standard weight, and the end of the pipe from which the welded junction protrudes is to be open. The thermocouple junction protrudes <sup>1</sup> 2 in (12.7 mm) from the open end of the pipe.

The ambient temperature during the tests was averaged according to the test reports and assumed 20 ◦C.

The software package (SP) ELCUT [35] was used to analyze the temperature distribution over the cross-section of the considered structures.

#### *2.1. Experiments on Bulkhead and Deck Structures*

The fire resistance of H-class bulkheads (H-0, H-60, H-120), A-class bulkheads (A-15, A-60) and deck (H-120) with mineral wool materials was investigated.

Fire tests of the H-0, H-60 and H-120 bulkheads were carried out at the Danish Institute of Fire and Security Technology (DIFT). The bulkheads were installed in a reinforced concrete frame and welded on four sides to the restraint frame. The dimensions of the structural core were following IMO Resolution A.754 (18). The test samples were tested with the insulation and the stiffeners toward the furnace.

The H-0 bulkhead has the following external dimensions: height 2480 mm, width 2420 mm, thickness 64.5/129.5 mm. The bulkhead consisted of a standard structural steel core insulated with Rockwool insulation (Hedehusene, Denmark), attached to the bulkhead with ø3 mm pins and ø28 mm washers. The pins on the level were located in 3 lines and a line on each of the stiffeners. The vertical center distance between the pins on the level was 400 mm along all lines. The vertical center distance between the pins on the stiffeners was 300 mm along all lines. The steel sheet thickness of 4.5 mm with the pins on the stiffeners at a distance of 600 mm was insulated with two layers of 30 mm Rockwool HC Firebatt (Hedehusene, Denmark) mineral wool with a density of 150 kg/m<sup>3</sup> .

The H-60 bulkhead has the following external dimensions: height 2480 mm, width 2420 mm, thickness 75/115 mm. The steel sheet thickness of 5 mm with the pins on the stiffeners at a distance of 600 mm was insulated with two layers of mineral wool: 40 mm Rockwool HC Wired Matt (Hedehusene, Denmark) with a density of 150 kg/m<sup>3</sup> and 30 mm Rockwool HC Firebatt with a density of 150 kg/m<sup>3</sup> . Installation of the insulation to the bulkhead is similar to the H-0 bulkhead.

The H-120 bulkhead has the following external dimensions: height 2480 mm, width 2420 mm, thickness 95/155 mm. The steel sheet thickness of 5 mm with the pins on the stiffeners at a distance of 600 mm was insulated with two layers of mineral wool: 40 mm Rockwool HC Wired Matt with density of 150 kg/m<sup>3</sup> and 50 mm Rockwool HC Firebatt with a density of 150 kg/m<sup>3</sup> . Installation of the insulation to the bulkhead is similar to the H-0 bulkhead.

The temperature on the test samples was determined by cable thermoelectric chromel– alumel thermocouples designed as described in IMO Resolution A.754 (18) [26] and mounted on the unheated surfaces of the sample (Figure 3). The location of the thermocouples for the H-60 bulkhead is the same as on the H-120 bulkhead.

**Figure 3.** (**a**) Location of thermocouples on bulkhead H-120. (**b**) Location of thermocouples on bulkhead H-0.

The A-15 and A-60 (sample No. 1 and sample No. 2) bulkheads were built following IMO Resolution A.754 (18) [26] and insulated on the stiffened side not exposed to the fire. The mineral wool panels are secured to the bulkhead plate through steel pins and washers welded with a pitch of 300 mm.

Fire tests of A-15 and A-60 (sample No. 1) class bulkheads were performed at RINA Services Spa (Genoa, Italy); fire test of A-60 (sample No. 2) class bulkhead was performed at FGBU VNIIPO EMERCOM of Russia (Balashikha, Moscow region, Russia). The bulkheads were tested in the vertical position exposing to the fire the uninsulated bulkhead side, mounted within a steel restraint frame having a refractory concrete lining 50 mm thick. The temperature on the test samples was measured by cable thermoelectric chromel–alumel thermocouples, installed in the amount of 7 pieces on the unheated surfaces of the sample.

The A-15 bulkhead has the following external dimensions: height 3020 mm, width 3020 mm, thickness 44.5/69.5 mm. The steel sheet thickness of 4.5 mm with the pins on the stiffeners at a distance of 600 mm was insulated with one layer of mineral wool: 40 mm PAROC Marine Fire Slab (Helsinki, Finland) with a density of 80 kg/m<sup>3</sup> .

The A-60 bulkhead (sample No. 1) has the following external dimensions: height 3020 mm, width 2420 mm, thickness 65/90 mm. The steel sheet thickness of 5 mm with the pins on the stiffeners at a distance of 600 mm was insulated with two layers of mineral wool: 60 mm and 25 mm PAROC Fire Slab (Helsinki, Finland) with a density of 100 kg/m<sup>3</sup> .

The A-60 bulkhead (sample No. 2) has the following external dimensions: height 2480 mm, width 2420 mm, thickness 54.5/79.5 mm. The steel sheet thickness of 4.5 mm with the pins on the stiffeners at a distance of 600 mm was insulated with two layers of 25 mm TIZOL-FLOT Fire (Yekaterinburg, Russia) with a density of 100 kg/m<sup>3</sup> .

Fire tests of the steel deck H-120 were carried out at the Fire Safety Scientific and Test Center of the FGBU VNIIPO EMERCOM of Russia (Balashikha, Moscow region, Russia). The temperature on the sample was measured by thermocouples, installed in the amount of 7 pieces on the unheated surface of the sample.

The H-120 deck has the following external dimensions: height 2440 mm, width 3040 mm, thickness 126/246 mm. The steel sheet thickness of 6 mm with the pins on the stiffeners at a distance of 600 mm was insulated with two layers of 60 mm Rockwool mineral wool panels with a density of 100 kg/m<sup>3</sup> .

#### *2.2. Simulation of Bulkhead and Deck Section Heating*

SP ELCUT allows solving tasks related to the heating of structures [36]. All calculations of the structures are performed by the finite element method based on the two-dimensional finite element model in the ELCUT software. To solve the task, it is necessary to specify the geometry, describe the properties of the medium and define the boundary conditions. The input of the task parameters consists of marks divided into three groups [35]:

Block marks that describe the material properties in the model;

Rib marks describing the boundary conditions on the outer and inner surfaces of the model;

Vertex marks that describe the anchoring conditions (boundary conditions) applied to certain points in the model.

In the simulation of heating, the thermal conductivity equation is used in the flat case (3) [37]:

$$\frac{\partial}{\partial \mathbf{x}} \left( \lambda\_x \frac{\partial T}{\partial \mathbf{x}} \right) + \frac{\partial}{\partial y} \left( \lambda\_y \frac{\partial T}{\partial y} \right) = -q - c\rho \times \frac{\partial T}{\partial t} \tag{3}$$

where *T* is the temperature in ◦C; *t* is the time in seconds; *λ* means the components of the thermal conductivity tensor in W/(m·K); *<sup>q</sup>* is the specific power of heat source in W/m<sup>3</sup> ; *c* is the specific heat capacity in J/(kg·K); and *<sup>ρ</sup>* is the density in kg/m<sup>3</sup> .

A number of boundary conditions, such as temperature, heat flow, convection and radiation, are set at the outer and inner boundaries of the computational domain. The value of *T*<sup>0</sup> is given as a linear function of coordinates. The heat flow is described by the following Relations (4) and (5) [35]:

$$F\_n = -q\_s \text{---} \text{on the outer border} \tag{4}$$

$$F\_n^+ - F\_n^- = -q\_s \text{--on the inner border} \tag{5}$$

where *F<sup>n</sup>* is the normal component of the density vector of heat flow, where "+" and "−" mean "left of the border" and "right of the border," respectively, in W/m<sup>2</sup> ; *q<sup>s</sup>* is the power surface of the source for the inner border, for the outer, the known value of heat flow through the border in W/m<sup>2</sup> .

Convective heat transfer is determined according to (6) [38]:

$$F\_{\rm n} = \mathfrak{a} \times \left(T - T\_0\right) \tag{6}$$

where *α* is the convective heat transfer coefficient in W/m<sup>2</sup> ·K; *T*<sup>0</sup> is the ambient temperature in K.

The radiation condition is set at the outer border of the model; the radiation heat transfer is determined according to (7) [35]:

$$F\_n = k\_{SB} \times \beta \times \left(T^4 - T\_0^4\right) \tag{7}$$

where *kSB* is the Stefan–Boltzmann constant in W/(m<sup>2</sup> · K 4 ); *β* is the surface absorption coefficient; and *T*<sup>0</sup> is the temperature of an absorbing medium in K.

Simulations were performed for bulkheads and deck under hydrocarbon and standard fire regimes.

Initial steel characteristics: steel grade D36 [39]; density 7800 kg/m<sup>3</sup> ; thermal conductivity and heat capacity are variable depending on temperature (values are taken from the program reference book). The boundary conditions are presented in Table 2.

**Table 2.** Boundary conditions set in the SP ELCUT.


Note: \* According to the test reports, the temperature measured by thermocouples in the furnace was determined as an absolute value, and the temperature on the unheated surface was recorded and displayed as the difference between the ambient temperature and the temperature on the unheated surface.

The characteristics of the mineral wool for the different bulkheads and deck are shown in Table 3. It is assumed that the density value does not change during heating. The value of heat capacity is assumed to be averaged for all types of mineral wool according to manufacturer's website and [41]; the trend of heat capacity change with temperature is assumed according to [42]. Moreover, the main influence on the heat transfer in the solid material layer has thermal conductivity [37].


**Table 3.** The main characteristics of mineral wool for structures.

Note: \* Sample No. 1; \*\* Sample No. 2.

#### **3. Results and Discussion**

#### *3.1. Experimental and Simulation Results*

For the H-0 bulkhead, the fire test was stopped at 122 min according to the requirements for this class of bulkheads (the limit condition for H-0 bulkheads is loss of integrity (E)). When the required time was reached, no smoke and flame penetration to the unheated side was observed, the integrity of the sample was preserved, and the deflection of the sample in the center of the bulkhead (60 mm) and the changing of the color of the open surface to yellow were recorded. According to the test results, it was found that the H-0 bulkhead with a steel sheet thickness of 4.5 mm, insulated with mineral wool with a thickness of 60/125 mm and a density of 150 kg/m<sup>3</sup> , has fire resistance under the action of a hydrocarbon fire regime for at least 30 min before reaching the parameter of thermal insulating capacity (I) and at least 120 min before reaching the parameter of loss of integrity due to the temperature increase on the unheated surface of the structure on average more than 140 ◦C. According to the DIFT report, the H-0 bulkhead may also be classified as H-30 regarding the experimental data obtained.

For the H-60 bulkhead, the fire test was stopped at 123 min when the critical temperature on the unheated surface of the structure reached an average of more than 140 ◦C (the technical customer's request extended the test), no smoke and flame penetration on the unheated side was observed, the integrity of the sample was preserved, and the deflection of the sample in the center of the bulkhead (42 mm) and the changing of the color of the open surface to yellow were recorded. According to the test results, it was found that the H-60 bulkhead with a steel sheet thickness of 5 mm, insulated with mineral wool with a thickness of 70/110 mm and a density of 150 kg/m<sup>3</sup> , has fire resistance under the action of a hydrocarbon fire regime for at least 120 min.

For the H-120 bulkhead, the fire test was stopped at 125 min when the critical temperature on the unheated surface of the structure reached an average of more than 140 ◦C (the technical customer's request extended the test), no smoke and flame penetration on the unheated side was observed, the integrity of the sample was preserved, and the deflection of the sample in the center of the bulkhead (24 mm) and the changing of the color of the open surface to yellow were recorded. According to the test results, it was found that the H-120 bulkhead with a steel sheet thickness of 5 mm, insulated with mineral wool with a thickness of 90/150 mm and a density of 150 kg/m<sup>3</sup> , has fire resistance under the action of a hydrocarbon fire regime for at least 120 min.

The H-class bulkheads' appearance before and after the fire test did not change, and the deflection at the center of the bulkheads did not reach the limit value of l/20 in each test [27]. For example, the heated and unheated sides before and after the fire test of H-120 bulkheads (Figures 4 and 5) and mineral wool after the fire test of H-120 and H-0 bulkheads (Figure 6) are shown.

**Figure 4.** (**a**) Heated side of H-120 bulkhead before fire test. (**b**) Heated side of H-120 bulkhead after fire test.

**Figure 5.** (**a**) H-120 bulkhead at the beginning of fire test. (**b**) H-120 bulkhead at the end of fire test.

**Figure 6.** (**a**) Mineral wool after fire test of H-120 bulkhead. (**b**) Mineral wool after fire test of H-0 bulkhead.

For the A-15 bulkhead, the fire test was stopped at 30 min according to the requirements. No smoke and flame penetration on the unheated side was observed, the sample's integrity was preserved, and the deflection of the sample in the center of the bulkhead (105 mm) was recorded. No cracks and holes in the sample were found. According to the test results, it was found that the A-15 bulkhead with a steel sheet thickness of 4.5 mm, insulated with mineral wool with a thickness of 40 mm and a density of 80 kg/m<sup>3</sup> , has fire resistance under the action of a standard fire regime for at least 15 min.

For the A-60 bulkhead (sample No. 1), the fire test was stopped at 60 min when the critical temperature on the unheated surface of the structure reached an average of more than 140 ◦C. No smoke and flame penetration on the unheated side was observed, the sample's integrity was preserved, and the deflection of the sample in the center of the bulkhead (70 mm) was recorded. No cracks and holes in the sample were found. According to the test results, it was found that the A-60 bulkhead (sample No. 1) with a steel sheet thickness of 5 mm, insulated with mineral wool with a thickness of 60/85 mm and a density of 100 kg/m<sup>3</sup> , has fire resistance under the action of a standard fire regime for at least 60 min.

For the A-60 bulkhead (sample No. 2), the fire test was stopped at 60 min according to the customer's requirements. No smoke and flame penetration on the unheated side was observed, and the integrity of the sample was preserved. No cracks, holes or other visible changes on the sample were found, and the deflection value was not measured. According to the test results, it was found that the A-60 bulkhead (sample No. 2) with a steel sheet thickness of 4.5 mm, insulated with mineral wool with a thickness of 50/75 mm and with a density of 100 kg/m<sup>3</sup> , has fire resistance under the action of a standard fire regime for at least 60 min.

Considered A-class bulkheads did not change their appearance before and after the fire test, and the deflection at the center of the bulkheads did not reach the limit value of l/20 in each test [27]. For example, the heated and unheated sides after the fire test of the A-15 bulkhead are shown (Figure 7).

**Figure 7.** (**a**) Heated side of A-15 bulkhead at the end of the fire test. (**b**) Unheated side of A-15 bulkhead at the end of the fire test.

For the deck H-120, the fire test was stopped at 125 min when the critical temperature on the unheated surface of the structure reached an average of more than 140 ◦C. No smoke and flame penetration on the unheated side was observed, and the integrity of the sample was preserved. No cracks, holes or other visible changes on the sample were found, and the deflection value was not measured (Figure 8). According to the test results, it was found that deck H-120, with a steel sheet thickness of 6 mm, insulated with mineral wool with a thickness of 120/240 mm and a density of 100 kg/m<sup>3</sup> , has fire resistance under the action of a hydrocarbon fire regime for at least 120 min.

Figure 9 shows the time–temperature curves of the bulkheads and deck during the fire test. The graph shows the averaged values of the difference between the values of thermocouples located directly on the unheated surface of the sample and the initial ambient temperature (20 ◦C, Table 3).

**Figure 8.** (**a**) Deck H-120 before the fire test. (**b**) Deck H-120 after the fire test.

**Figure 9.** Temperature curves of experimental samples during fire tests.

As a result of the simulation, visualizations of the heating of the experimental bulkheads and deck were obtained (Figure 10). The location of the thermocouples on the structures is shown in the analytical model. Each analytical model represents <sup>1</sup> 4 of the structure since it consists of similar and repeating fragments. For H-class bulkheads and H-120 deck, the fire exposure was from the mineral wool side, and for A-class bulkheads, from the steel plate side.

Temperature scale for standard fire regime

**Figure 10.** Analytical models of structures and thermocouple locations and visualization of the heating of bulkhead and deck structures.

The temperature–time dependences at the thermocouple location on the unheated surface were obtained for H-class bulkheads and deck H-120 (Figure 11).

The graph shows the averaged values of the difference between the values of thermocouples located directly on the unheated surface of the sample and the initial ambient temperature (20 ◦C, Table 3). The different location of the thermocouples over the crosssection of the samples is shown in Figure 10. Heat and mass transfer processes were not considered in the modeling.

The results of the simulation show excellent correlation of the results (difference in values not more than 5%), except for the results for the H-0 bulkhead (25% in the range of 20 to 30 min), which has a smaller plate thickness (60 mm) compared to the other samples. Mineral wool is a dry fire retardant; however, it contains organic substances and water (Table 3). At a sharp temperature effect in the hydrocarbon fire regime in the range from 30 to 100 ◦C, the processes of heat and mass transfer are intensified, which may explain the excess of simulation results compared with the experimental values of temperatures.

Analysis of Figure 11 shows that the graph for the H-0 bulkhead grows more rapidly because the bulkhead warms up faster due to the fact that it has a smaller plate thickness (60/125 mm) at the same density (150 kg/m<sup>3</sup> ). The graph for the deck H-120 with lower density (100 kg/m<sup>3</sup> ) during the first 30 min shows higher temperature values compared to the H-120 bulkhead (150 kg/m<sup>3</sup> ); after 45 min, due to the higher insulation thickness (120/240 mm), the graph for the deck H-120 shows a smoother temperature increase until the limit value is reached.

The temperature–time dependences at the thermocouple location on the unheated surface were obtained for A-class bulkheads (Figure 12).

Analysis of Figure 12 shows that the graph for the A-15 bulkhead grows more rapidly because the bulkhead warms up faster due to the fact that it has a smaller plate thickness (40 mm) and a lower density (80 kg/m<sup>3</sup> ) while the A-60 bulkheads have higher values: density 100 kg/m<sup>3</sup> and plate thickness 60/85 mm for sample No. 1 and 50/75 mm for sample No. 2. Samples No. 1 and No. 2 for A-60 bulkheads with a density of 100 kg/m<sup>3</sup> have similar dynamics of temperature increase up to 30 min, then sample No. 1 continues to heat uniformly, while sample No. 2, which has a plate thickness of 10 mm less than the thickness of sample No. 1, increases sharply and reaches equilibrium state after 40 min of heating.

**Figure 12.** Experimental and simulated temperature curves of samples during the fire test under the standard fire regime.

In the example of the H-0 bulkhead, the deflection in the center of the considered structure under the thermal load was calculated in SP ELCUT using the connection of tasks of unsteady heat transfer and mechanical stresses and strains, which resulted in a deformation diagram shifted by 63 mm relative to the original position (Figure 13).

**Figure 13.** Deformation diagram of H-0 bulkhead under heat load.

According to [27], the limit value of deflection at the center of the bulkhead is determined according to (8):

$$
\Delta = \frac{l}{20} = \frac{2480}{20} = 124 \text{ mm} \tag{8}
$$

Thus, the deflection value obtained during the experiment (60 mm) and from the simulation (63 mm) does not exceed the acceptable value and confirms that the H-0 bulkhead subjected to high-temperature fire exposure maintains its integrity throughout the test.

#### *3.2. Discussion*

The calculated temperature values on the considered structures, obtained from the simulation results in the SP ELCUT, perfectly correlate with the experimentally obtained temperature values in any time period. In the example of the H-0 bulkhead, the thickness of used mineral wool was evaluated, and other variants of the rate of consumption of mineral wool under the hydrocarbon fire regime were presented (Figure 14). The choice

of the bulkhead is justified by the maximum temperatures obtained from the experiment and simulation. The graph shows the averaged values of the difference between the values of thermocouples located directly on the unheated surface of the sample and the initial ambient temperature (20 ◦C, Table 3). The different locations of the thermocouples over the cross-section of the samples are shown in Figure 10. The H-0 bulkhead is also certified as H-30. According to the initial data, the H-0 bulkhead has two layers of mineral wool with a total thickness of 60 mm (2 <sup>×</sup> 30 mm) with a density of 150 kg/m<sup>3</sup> . One of the ways to reduce the consumption of mineral plates is to increase their density. For example, when choosing the density of mineral wool as 240 kg/m<sup>3</sup> (PAROC mineral wool [43]), the temperature at 30 min is reduced by 40 ◦C, which shows the overconsumption of used fire protection. There are two variants to reduce the thickness of mineral wool with a density of 240 kg/m<sup>3</sup> : using two layers of thickness of 25 mm and two layers of thickness of 20 mm. At a total thickness of 40 mm (2 × 20 mm), the temperature at 30 min reaches 138 ◦C, which shows optimal thickness use, providing the required fire protection efficiency in hydrocarbon fire mode.

**Figure 14.** Variations of flame-retardant application for H-0 bulkhead.

Endothermic mats with high fire-resistance limits and high cost relative to mineral wool are also used as insulation systems in O&G [44]. Thermophysical characteristics were taken for flexible endothermic mat "3M Interam" with a thickness of 20 mm with basalt fiber and endothermic ingredients (Table 4).

**Table 4.** Coefficients of thermal conductivity and heat capacity of the endothermic mat "3M Interam" as a function of temperature [45].


When using an endothermic mat with a thickness of 40 mm, the temperature at 30 min reaches 37 ◦C, which proves the need to reduce the consumption of the used insulation system. When reducing the thickness of the endothermic mat to 20 mm, the temperature at 30 min reaches 139 ◦C, which proves the use of optimal thickness, at which the required fire protection efficiency in hydrocarbon fire mode is provided.

The values of coefficients of thermal conductivity and heat capacity of mineral wool manufacturers Rockwool (1), PAROC (2) and TIZOL (3) were clarified (Table 5). The calculated values of thermophysical characteristics obtained from the simulation correlate with the values in Table 3. For temperatures above 400 ◦C, the obtained values require experimental confirmation but can be used in solving thermal engineering tasks with unsteady thermal conductivity.

**Table 5.** Calculation coefficients of thermal conductivity and heat capacity of mineral wools.


Analysis of Table 5 shows that the best characteristics (the lowest thermal conductivity in the range from 0 to 1000 ◦C) to perform the functions of fire protection and thermal insulation have material 1 (Rockwool). As stated in Section 2, the heat capacity values were given the same and averaged for all types of mineral wool due to the lack of accurate data at elevated temperatures from manufacturers.

#### **4. Conclusions**

Test methods of the fire resistance of steel structures for hydrocarbon fuel transportation facilities are similar to the requirements of onshore structures of the oil and gas complex. The same parameters under different fire regimes are applied: loss of integrity and thermal insulating capacity. Based on experimental results, simulation of the fire resistance of bulkheads of different classes and decks for an offshore platform was carried out. It was found that to obtain the required fire-resistance limits of bulkheads in standard fire conditions (A-class), mineral wool with a density of 80–100 kg/m<sup>2</sup> and fire protection material consumption of 40 to 85 mm (plate thickness) should be used; hydrocarbon mode (H-class) requires the use of the densest mineral wool (from 100 kg/m<sup>2</sup> ) with a material consumption of 60–150 mm. Thus, to protect steel decks and bulkheads in a hydrocarbon fire with a structural steel thickness of 4.5–5 mm, it is necessary to use 30–40% more thermal insulation and apply the highest density of fire-retardant material compared to the standard fire.

Simulations have shown that constructing the H-0 bulkhead certified as H-30 (for loss of integrity and thermal insulating capacity) and H-0 (for loss of integrity) with mineral wool with a density of 150 kg/m<sup>3</sup> and a thickness of 60 mm is not optimal in relation to fire protection overage.

The simulated H-0 bulkhead with mineral wool with a density of 240 kg/m<sup>3</sup> and an insulation thickness of 40 mm and endothermic mat with a density of 865 kg/m<sup>3</sup> and a thickness of 20 mm can reduce the consumption of fire protection by 33% and 66%, respectively, providing the required fire resistance H-30. It is expected in the future to use fire protection and thermal insulation plates containing a combination of super-thin basalt fiber and ceramic fibers, designing a high fire-resistance rating and an adequate final product cost.

The obtained values of the coefficients of thermal conductivity and heat capacity for mineral wool can be used in the calculation of structures for fire resistance with the considered type of fire protection in the temperature range from 0 to 1000 ◦C.

**Author Contributions:** Conceptualization, M.G.; data curation, D.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation under the strategic academic leadership program "Priority 2030" (Agreement 075-15-2021-1333 dated 30 September 2021).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Testing laboratories of the FGBU VNIIPO EMERCOM of Russia, Danish Institute of Fire and Security Technology and RINA Services Spa.

**Acknowledgments:** The authors would like to thank Nikolai Ivanovich Vatin, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia, for valuable and profound comments.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

